[Asinkrit]

Самый простой и быстрый способ)

Код:

procedure TForm1.Button1MouseMove(Sender: TObject; Shift: TShiftState; X,
  Y: Integer);
const
  SC_DRAGMOVE = $F012;
begin
  ReleaseCapture;
  Perform(WM_SYSCOMMAND, SC_DRAGMOVE, 0);
end;