Born in Glasgow, the 21-year-old playmaker began his footballing career with Dundee United before joining the Baggies for an undisclosed fee in January 2012.
During his time at the Hawthorns, the Scotland U21 international has spent spells out on loan with Portsmouth and MK Dons, where he made a total of 28 starts and scored two goals. He has yet to make his first-team bow for West Brom.
Lee Clark feels that Allan will give his side an extra dimension in the middle of the pitch and that he is an able replacement for former loanee Ravel Morrison.
"Scott has been on our radar for some time and is a very talented player," said the Blues boss.
"He can go past people and he can make a goal and score a goal. He also likes to get on the ball and make things happen. He can play in a wide area, but I’m predominantly bringing him in to be that attacking midfield player in behind the strikers.
"It’s been common knowledge that I’ve been looking for this type of player – a Ravel Morrison-type midfield player.
"Obviously we’ve tried to bring Ravel back from West Ham but the indications are that after doing so well with us, he’s carried that on in the pre-season with West Ham and he’s impressed the manager and the coaches there, so they weren’t in a rush to make a decision."
Got your 2013/14 season ticket yet? Click here