Allan holds the record for being the youngest player to feature in a British first-team match after he made his debut for the Scottish outfit against Livingston last year aged 14 years and 199 days.
The forward, now 15, has penned a four-year deal at Molineux, and his former boss Jimmy Boyle has tipped Allan to be a success at the Championship club.
The 47-year-old is quoted by the Express & Star as saying: "This is great news for the boy. Jordan's very focused and hard-working. Scoring goals is what he does best. He's a natural finisher.
"He's a team player, listens to what he is being told and has a great attitude. I know that he has a great family behind him and he will have no problem making this move."
Allan is likely to spend time in Wolves' development setup before featuring for the first team.