AnimatedPositioned

bool _first = true;

double _left = 20;
double _top = 20;
double _right = 20;
double _bottom = 20;

@override
Widget build(BuildContext context) {
  return Column(
    mainAxisAlignment: MainAxisAlignment.center,
    children: <Widget>[
      Container(
        height: 300,
        child: Stack(
          children: <Widget>[
            AnimatedPositioned(
              duration: const Duration(milliseconds: 500),
              curve: Curves.fastOutSlowIn,
              left: _left,
              top: _top,
              right: _right,
              bottom: _bottom,
              child: Container(
                color: Colors.blue,
              ),
            ),
          ],
        ),
      ),
      SizedBox(height: 20,),
      RaisedButton(
        child: const Text('CLICK ME!'),
        onPressed: () {
          setState(() {
            _left   = _first ?  10 : 20;
            _top    = _first ?  70 : 20;
            _right  = _first ?  10 : 20;
            _bottom = _first ?  70 : 20;

            _first = !_first;
          });
        },
      ),
    ],
  );
}