How to achieve rounded corners on new OutlinedButton widget in Flutter?

You can use OutlinedButton.styleFrom property:

OutlinedButton(
   style: OutlinedButton.styleFrom(
      shape: RoundedRectangleBorder(
         borderRadius: BorderRadius.circular(18.0),
      ),
      side: BorderSide(width: 2, color: Colors.green),
   ),
   onPressed: () {},
   child: Text('Button'),
)

From the source code

 /// All parameters default to null, by default this method returns
 /// a [ButtonStyle] that doesn't override anything.
 ///
 /// For example, to override the default shape and outline for an
 /// [OutlinedButton], one could write:
 ///
 /// ```dart
 /// OutlinedButton(
 ///   style: OutlinedButton.styleFrom(
 ///      shape: StadiumBorder(),
 ///      side: BorderSide(width: 2, color: Colors.green),
 ///   ),
 /// )
 /// ```