diff --git a/python/PyQt6/core/auto_generated/processing/qgsprocessingoutputs.sip.in b/python/PyQt6/core/auto_generated/processing/qgsprocessingoutputs.sip.in
index 02d014c5a9fa..7e50b0438f00 100644
--- a/python/PyQt6/core/auto_generated/processing/qgsprocessingoutputs.sip.in
+++ b/python/PyQt6/core/auto_generated/processing/qgsprocessingoutputs.sip.in
@@ -135,6 +135,27 @@ Returns a string version of the parameter output ``value`` (if possible).
 :return: - value converted to string
          - ok: will be set to ``True`` if value could be represented as a string.
 
+.. seealso:: :py:func:`valueAsFormattedString`
+
+
+.. versionadded:: 3.36
+%End
+
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+%Docstring
+Returns a HTML string version of the parameter output ``value`` (if possible).
+
+By default this will return the same value as :py:func:`~QgsProcessingOutputDefinition.valueAsString`.
+
+:param value: value to convert
+:param context: processing context
+
+:return: - value converted to string
+         - ok: will be set to ``True`` if value could be represented as a string.
+
+.. seealso:: :py:func:`valueAsString`
+
+
 .. versionadded:: 3.36
 %End
 
@@ -328,6 +349,8 @@ Constructor for QgsProcessingOutputHtml.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
 };
 
 
@@ -464,6 +487,9 @@ Constructor for QgsProcessingOutputFolder.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
+
 };
 
 class QgsProcessingOutputFile : QgsProcessingOutputDefinition
@@ -489,6 +515,9 @@ Constructor for QgsProcessingOutputFile.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
+
 };
 
 class QgsProcessingOutputConditionalBranch : QgsProcessingOutputDefinition
diff --git a/python/core/auto_generated/processing/qgsprocessingoutputs.sip.in b/python/core/auto_generated/processing/qgsprocessingoutputs.sip.in
index 02d014c5a9fa..7e50b0438f00 100644
--- a/python/core/auto_generated/processing/qgsprocessingoutputs.sip.in
+++ b/python/core/auto_generated/processing/qgsprocessingoutputs.sip.in
@@ -135,6 +135,27 @@ Returns a string version of the parameter output ``value`` (if possible).
 :return: - value converted to string
          - ok: will be set to ``True`` if value could be represented as a string.
 
+.. seealso:: :py:func:`valueAsFormattedString`
+
+
+.. versionadded:: 3.36
+%End
+
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+%Docstring
+Returns a HTML string version of the parameter output ``value`` (if possible).
+
+By default this will return the same value as :py:func:`~QgsProcessingOutputDefinition.valueAsString`.
+
+:param value: value to convert
+:param context: processing context
+
+:return: - value converted to string
+         - ok: will be set to ``True`` if value could be represented as a string.
+
+.. seealso:: :py:func:`valueAsString`
+
+
 .. versionadded:: 3.36
 %End
 
@@ -328,6 +349,8 @@ Constructor for QgsProcessingOutputHtml.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
 };
 
 
@@ -464,6 +487,9 @@ Constructor for QgsProcessingOutputFolder.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
+
 };
 
 class QgsProcessingOutputFile : QgsProcessingOutputDefinition
@@ -489,6 +515,9 @@ Constructor for QgsProcessingOutputFile.
 Returns the type name for the output class.
 %End
     virtual QString type() const;
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok /Out/ ) const;
+
+
 };
 
 class QgsProcessingOutputConditionalBranch : QgsProcessingOutputDefinition
diff --git a/src/core/processing/qgsprocessingoutputs.cpp b/src/core/processing/qgsprocessingoutputs.cpp
index 0ca41aeb870a..ccc449ef99af 100644
--- a/src/core/processing/qgsprocessingoutputs.cpp
+++ b/src/core/processing/qgsprocessingoutputs.cpp
@@ -18,6 +18,9 @@
 #include "qgsprocessingoutputs.h"
 #include "qgsvariantutils.h"
 
+#include <QUrl>
+#include <QDir>
+
 QgsProcessingOutputDefinition::QgsProcessingOutputDefinition( const QString &name, const QString &description )
   : mName( name )
   , mDescription( description )
@@ -40,6 +43,11 @@ QString QgsProcessingOutputDefinition::valueAsString( const QVariant &value, Qgs
   return QString();
 }
 
+QString QgsProcessingOutputDefinition::valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok ) const
+{
+  return valueAsString( value, context, ok );
+}
+
 QgsProcessingOutputVectorLayer::QgsProcessingOutputVectorLayer( const QString &name, const QString &description, QgsProcessing::SourceType type )
   : QgsProcessingOutputDefinition( name, description )
   , mDataType( type )
@@ -71,6 +79,17 @@ QgsProcessingOutputHtml::QgsProcessingOutputHtml( const QString &name, const QSt
   : QgsProcessingOutputDefinition( name, description )
 {}
 
+QString QgsProcessingOutputHtml::valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok ) const
+{
+  if ( value.type() == QVariant::String && !value.toString().isEmpty() )
+  {
+    ok = true;
+    return QStringLiteral( "<a href=\"%1\">%2</a>" ).arg( QUrl::fromLocalFile( value.toString() ).toString(), QDir::toNativeSeparators( value.toString() ) );
+  }
+
+  return valueAsString( value, context, ok );
+}
+
 QgsProcessingOutputNumber::QgsProcessingOutputNumber( const QString &name, const QString &description )
   : QgsProcessingOutputDefinition( name, description )
 {}
@@ -116,10 +135,32 @@ QgsProcessingOutputFolder::QgsProcessingOutputFolder( const QString &name, const
   : QgsProcessingOutputDefinition( name, description )
 {}
 
+QString QgsProcessingOutputFolder::valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok ) const
+{
+  if ( value.type() == QVariant::String && !value.toString().isEmpty() )
+  {
+    ok = true;
+    return QStringLiteral( "<a href=\"%1\">%2</a>" ).arg( QUrl::fromLocalFile( value.toString() ).toString(), QDir::toNativeSeparators( value.toString() ) );
+  }
+
+  return valueAsString( value, context, ok );
+}
+
 QgsProcessingOutputFile::QgsProcessingOutputFile( const QString &name, const QString &description )
   : QgsProcessingOutputDefinition( name, description )
 {}
 
+QString QgsProcessingOutputFile::valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok ) const
+{
+  if ( value.type() == QVariant::String && !value.toString().isEmpty() )
+  {
+    ok = true;
+    return QStringLiteral( "<a href=\"%1\">%2</a>" ).arg( QUrl::fromLocalFile( value.toString() ).toString(), QDir::toNativeSeparators( value.toString() ) );
+  }
+
+  return valueAsString( value, context, ok );
+}
+
 QgsProcessingOutputMapLayer::QgsProcessingOutputMapLayer( const QString &name, const QString &description )
   : QgsProcessingOutputDefinition( name, description )
 {}
diff --git a/src/core/processing/qgsprocessingoutputs.h b/src/core/processing/qgsprocessingoutputs.h
index f79e83190204..bbaff8db44f5 100644
--- a/src/core/processing/qgsprocessingoutputs.h
+++ b/src/core/processing/qgsprocessingoutputs.h
@@ -143,10 +143,28 @@ class CORE_EXPORT QgsProcessingOutputDefinition
      * \param ok will be set to TRUE if value could be represented as a string.
      * \returns value converted to string
      *
+     * \see valueAsFormattedString()
+     *
      * \since QGIS 3.36
      */
     virtual QString valueAsString( const QVariant &value, QgsProcessingContext &context, bool &ok SIP_OUT ) const;
 
+    /**
+     * Returns a HTML string version of the parameter output \a value (if possible).
+     *
+     * By default this will return the same value as valueAsString().
+     *
+     * \param value value to convert
+     * \param context processing context
+     * \param ok will be set to TRUE if value could be represented as a string.
+     * \returns value converted to string
+     *
+     * \see valueAsString()
+     *
+     * \since QGIS 3.36
+     */
+    virtual QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok SIP_OUT ) const;
+
   protected:
 
     //! Output name
@@ -322,6 +340,7 @@ class CORE_EXPORT QgsProcessingOutputHtml : public QgsProcessingOutputDefinition
      */
     static QString typeName() { return QStringLiteral( "outputHtml" ); }
     QString type() const override { return typeName(); }
+    QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok SIP_OUT ) const override;
 };
 
 
@@ -439,6 +458,8 @@ class CORE_EXPORT QgsProcessingOutputFolder : public QgsProcessingOutputDefiniti
      */
     static QString typeName() { return QStringLiteral( "outputFolder" ); }
     QString type() const override { return typeName(); }
+    QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok SIP_OUT ) const override;
+
 };
 
 /**
@@ -461,6 +482,8 @@ class CORE_EXPORT QgsProcessingOutputFile : public QgsProcessingOutputDefinition
      */
     static QString typeName() { return QStringLiteral( "outputFile" ); }
     QString type() const override { return typeName(); }
+    QString valueAsFormattedString( const QVariant &value, QgsProcessingContext &context, bool &ok SIP_OUT ) const override;
+
 };
 
 /**
diff --git a/tests/src/analysis/testqgsprocessing.cpp b/tests/src/analysis/testqgsprocessing.cpp
index aead5cf5c4d0..7e5283d93059 100644
--- a/tests/src/analysis/testqgsprocessing.cpp
+++ b/tests/src/analysis/testqgsprocessing.cpp
@@ -12863,6 +12863,10 @@ void TestQgsProcessing::testOutputs()
             QStringLiteral( "/home/test/test.html" ) );
   QVERIFY( ok );
   ok = false;
+  QCOMPARE( outputHtml.valueAsFormattedString( QStringLiteral( "/home/test/test.html" ), context, ok ),
+            QStringLiteral( "<a href=\"file:///home/test/test.html\">/home/test/test.html</a>" ) );
+  QVERIFY( ok );
+  ok = false;
   QCOMPARE( outputHtml.valueAsString( QVariant(), context, ok ),
             QStringLiteral( "NULL" ) );
   QVERIFY( ok );
@@ -12873,6 +12877,10 @@ void TestQgsProcessing::testOutputs()
             QStringLiteral( "/home/test/test.txt" ) );
   QVERIFY( ok );
   ok = false;
+  QCOMPARE( outputFile.valueAsFormattedString( QStringLiteral( "/home/test/test.txt" ), context, ok ),
+            QStringLiteral( "<a href=\"file:///home/test/test.txt\">/home/test/test.txt</a>" ) );
+  QVERIFY( ok );
+  ok = false;
   QCOMPARE( outputFile.valueAsString( QVariant(), context, ok ),
             QStringLiteral( "NULL" ) );
   QVERIFY( ok );
@@ -12883,6 +12891,10 @@ void TestQgsProcessing::testOutputs()
             QStringLiteral( "/home/test" ) );
   QVERIFY( ok );
   ok = false;
+  QCOMPARE( outputFolder.valueAsFormattedString( QStringLiteral( "/home/test" ), context, ok ),
+            QStringLiteral( "<a href=\"file:///home/test\">/home/test</a>" ) );
+  QVERIFY( ok );
+  ok = false;
   QCOMPARE( outputFolder.valueAsString( QVariant(), context, ok ),
             QStringLiteral( "NULL" ) );
   QVERIFY( ok );