The 22-year-old spent the first half of last season on loan at Highbury, scoring seven goals in 22 games, including a hat-trick against Leicester City in the Papa John’s Trophy.
He was then loaned to Peterborough United in January, making seven Championship appearances.
Torquay-born Morton has spent his whole professional career at West Brom. He never made a senior appearance but did feature for their Under-21s in the Papa John's Trophy.
His other loan spells were at Braintree Town, Northampton Town and Lincoln City, playing in their League One play-off final defeat by Blackpool.
Chairman Andy Pilley told the club website: “We are delighted to have Callum back in the building. He made a great impression on the squad and fans when he was last here, so it’s brilliant that he’s ours to keep.
"We pushed the boat out to get him back and had to fight off multiple clubs to do so as he was one of the key targets we wanted to focus on this window.
" I’d like to place on record our thanks to West Bromwich Albion for their assistance in making the deal happen. "
He is the fifth signing for new head coach Scott Brown, who said: "Callum is a fantastic player, who has impressed not only the staff here in the past but also the fans.
"His pace will make him a great addition up at the top of the park as well as his awareness and we know he’s a top player to bring to the club."
Morton said: "I am delighted to get the deal done. It has been in the pipeline for a few weeks now and I am just buzzing to be back.
"I was here for 4-5 months. The way it ended saw me go elsewhere and in hindsight it might not have been the best decision but I have no regrets.
“Knowing players here was important and it just helps for a seamless transition
“It feels like a completely different club to what I came into last season, and this time around I will be getting a full pre-season under my belt."