How to change background color of Elevated Button in Flutter from function?

You can style ElevatedButton by using the styleFrom static method or the ButtonStyle class. The first one is more convenience than the second one.

Using styleFrom to style an ElevatedButton:

ElevatedButton(
      child: Text('Button'),
      onPressed: () {},
      style: ElevatedButton.styleFrom({
           Color primary, // set the background color 
           Color onPrimary, 
           Color onSurface, 
           Color shadowColor, 
           double elevation, 
           TextStyle textStyle, 
           EdgeInsetsGeometry padding, 
           Size minimumSize, 
           BorderSide side, 
           OutlinedBorder shape, 
           MouseCursor enabledMouseCursor, 
           MouseCursor disabledMouseCursor, 
           VisualDensity visualDensity, 
           MaterialTapTargetSize tapTargetSize, 
           Duration animationDuration, 
           bool enableFeedback
     }),
),

Example:

ElevatedButton(
            child: Text('Button'),
            onPressed: () {},
            style: ElevatedButton.styleFrom(
                primary: Colors.purple,
                padding: EdgeInsets.symmetric(horizontal: 50, vertical: 20),
                textStyle: TextStyle(
                fontSize: 30,
                fontWeight: FontWeight.bold)),
),

Using ButtonStyle to style an ElevatedButton:

style: ButtonStyle({
  MaterialStateProperty<TextStyle> textStyle,    
  MaterialStateProperty<Color> backgroundColor,   
  MaterialStateProperty<Color> foregroundColor, 
  MaterialStateProperty<Color> overlayColor, 
  MaterialStateProperty<Color> shadowColor, 
  MaterialStateProperty<double> elevation, 
  MaterialStateProperty<EdgeInsetsGeometry> padding, 
  MaterialStateProperty<Size> minimumSize, 
  MaterialStateProperty<BorderSide> side, 
  MaterialStateProperty<OutlinedBorder> shape, 
  MaterialStateProperty<MouseCursor> mouseCursor,    
  VisualDensity visualDensity, 
  MaterialTapTargetSize tapTargetSize, 
  Duration animationDuration, 
  bool enableFeedback
})

Example

ElevatedButton(
            child: Text('Button'),
            onPressed: () {},
            style: ButtonStyle(
                backgroundColor: MaterialStateProperty.all(Colors.red),
                padding: MaterialStateProperty.all(EdgeInsets.all(50)),
                textStyle: MaterialStateProperty.all(TextStyle(fontSize: 30))),
),