Griffiths has scored 14 goals this season after returning to Easter Road from Wolves for a second loan spell and made his Scotland debut against Luxembourg in November.
McGivern, 23, has made 14 appearances since arriving from Manchester City on loan in August.
Manager Pat Fenlon told Hibernian's official website: "We are delighted to be able to keep both players until the end of the season.
"Both Leigh and Ryan have made massive contributions to the team and have been good for us.
"We've already said that we would do everything we could to keep them at Hibernian and fortunately all that hard work has come to fruition.
"This news gives everybody connected to the club a boost as we return after the winter break for Saturday's home game against Dundee."