The 22-year-old midfielder, who never made a first-team appearance for the West Midlands club, has moved to Easter Road on a two-year deal.
Allan was previously linked with a move to Scottish Championship rivals Rangers, the club he supported as a boy.
But he said: “The move here to Hibs ticks all the boxes. At this point in my career, I had my mind set on a move back home to Scotland and I want to play football as regularly as possible.
"I'm an ambitious player and I want to achieve success here with Hibs. I've been impressed with what the manager has said and I want to help the club get back into the Scottish Premiership.
“I’ve learned a lot from my time down south, personally and professionally, and this is a challenge that I'm looking forward to."
Allan spent last season on loan at Birmingham City, playing just five times as Lee Clark’s side narrowly avoided relegation from the Championship on goal difference.
He previously spent time on loan at Portsmouth on two occasions, as well as League One MK Dons, after signing for West Brom from Dundee United in 2012.
The Glasgow-born player began his career at Dundee, with a brief loan spell at Forfar Athletic, and made his debut for Scotland’s Under 21s against Norway in August 2011.
Hibs boss Alan Stubbs said: "We're delighted that we've been able to add Scott to our squad - he is a top-quality player with immense potential.
"He's young, but has already gained a lot of experience so he will be equipped for the demands of the upcoming season.”