Keogh has made 33 appearances in all competitions for the Championship promotion hopefuls this season.
"From stepping in the door just over two years ago, Andy has had a huge impact for us," manager Mick McCarthy's told the club's official website.
"He's a striker but he's also played wide left and wide right when required as good if not better than anyone else and always puts a real good shift in.
"There's always been interest in Andy from other clubs and all the managers I speak to like him.
"There have been a couple of occasions when he's had a rocky relationship with the supporters and perhaps hasn't quite been appreciated for all the graft he puts in.
"But all he ever wanted to do when he sat down in the office with me was to sign and stay on here. He loves it at Wolves and wants to play for this club and I think that's fantastic."
If Wolves, who are top of the Championship, win promotion to the Premier League while Keogh is at the club then the Iron stand to receive an extra £250,000 as part of the deal that took the Irish forward to Molineux. There is also a 15 per cent sell-on clause.