Griffiths has scored 14 goals on loan at Easter Road so far this season made his Scotland debut against Luxembourg in November.
McGivern, 23, has made 14 appearances since arriving on loan in August.
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."
Hibs last week said Griffiths would be the subject of a private disciplinary process as police began investigating an alleged racist tweet sent by the 22-year-old.
The lifelong Hibernian supporter, whose Wolves contract expires at the end of the season, had happier discussions with the club on Wednesday.
Griffiths said: "This season has been the most enjoyable of my career so far and I'm really pleased to be staying at Hibs."
Hibs remain in talks over extending a third loan spell with the future of Honduras midfielder Jorge Claros in the hands of parent club Motagua.
But they tied up a third deal on Wednesday as second-choice goalkeeper Sean Murdoch extended his contract until May.
Fenlon said: "This was another deal we were keen to tie up and Sean has been a good professional around the club.
"He has been on the bench and made a positive contribution in training sessions. We're pleased he will continue to provide experienced cover for Ben Williams."