The 17-year-old scored for the League One side against Manchester United at Old Trafford back in September, in the Carabao Cup
He has made 15 appearances for them in the league this term and passed a medical at Compton today before putting pen to paper.
“It’s amazing to be part of the pack. It feels incredible to have such a prestigious badge on the front of my shirt," said Matheson.
“Wolves is such a great club, giving constant opportunities in and around the first-team for players my age. That was something that attracted me and I’m looking forward to having that opportunity.
“The facilities are amazing, they are second-to-none. You’ve got world class pitches, coaches, facilities for anything and everything. It’s the best footballing place I’ve ever been to.
“It’s always a big factor when you can see that there are opportunities there for young players. You know, I am still 17, I’ve hopefully got a long playing career in football and hope Wolves can give me some opportunities that I can grasp in the palm of my hand.
“Regardless of if I’m playing for Rochdale or Wolves, I’ll always give 110 per cent, but I can’t wait to wear the badge for the first time in a proper game.”
Matheson is also an England under-18s player, and Wolves sporting director Kevin Thelwell said: "Our recruitment team have watched Luke since he made his debut at 15.
"He’s still only 17 and has made a lot of appearances for Rochdale in League One, which is a very good standard, and had strong games in the cups, particularly this season against Manchester United and Newcastle United."
Wolves boss Nuno Espirito Santo added: "Luke is going back to Rochdale.
"He is going to finish the season there. He is a young boy.
"He has already done good things for his age, so he is going back to Rochdale.
"He will join us in the summer. For his age, he has scored at a tough stadium to do so, and we expect good things."