The 20-year-old will link up with the Dons until late October and will be eligible to play in this afternoon’s game with Crewe Alexandra, subject to approval from the Football League.
Allan, who has made 10 appearances for Scotland U-21s, will be available for the tough games with Coventry City, Portsmouth, Preston North End and Stevenage before playing his final game away at Crawley Town on Tuesday 23rd October.
Glasgow-born Allan started his career at Dundee United and signed his first professional deal with the Scottish club in January 2008.
During his time at Dundee, the 5ft 9in midfielder enjoyed a three-month spell on loan at Forfar where he scored once in three appearances.
After returning to United, Allan went on to make nine appearances, including his debut in the Europa League tie with Slask Wroclaw in July 2011, before agreeing a deal to join West Brom in January 2012 after leaving the Terrors.
With first-team chances limited, Allan joined Portsmouth on a youth loan in February 2012 and made his English football debut in Pompey's 0-0 draw with Leeds United.
After extending his stay with the Hampshire-club, Allan went on to make 15 appearances and netted on one occasion before returning to the Baggies.
Speaking to mkdons.com, Allan revealed he is delighted to be joining the Dons and is looking forward to getting started.
He said: "I'm very happy to be able to sign here. The team plays very good football and I'm very excited about being part of that."
"The fans can expect a lot of creativity from me and hopefully I can make things happen."
Robinson also had a few words to say about his new playmaker, a player he tried to sign in earlier in the summer.
He added: "I've brought him here because of his ability to play football. He's a tremendous talent and somebody I know that can unlock doors and play as the number ten or out wide.
"When Mick Harford first came in we looked at him and tried to get him in. Honestly, I thought Scott might have been out of our league as there's five clubs in the Championship trying to sign him.
"But I made the phone call, everyone at West Brom was excellent and when they heard that we were interested I think they felt we were the right Club for him to come too."