AFC Bournemouth have signed Christian Atsu from Chelsea on a season-long loan deal.
Midfielder Miguel Pallardo has signed a new one-year deal with newly-promoted Hearts while Danny Wilson leaves.
The Manchester United centre-back joined Blues on transfer deadline day in January on a deal scheduled to run until the end of the season.
However, he lasted just 14 minutes of his debut in a 3-3 draw against Derby at St Andrew's on February 1 before leaving the field on a stretcher having sustained ankle ligament damage.
Thorpe returned to United for treatment on the injury, where he has remained since.
Birmingham boss Lee Clark still retained some hope of seeing the 21-year-old return to action in a City shirt before the end of the season, but that has now been extinguished with the loan deal formally concluded.
Manchester United reserve coach Warren Joyce told the Premier League club's official website: "It's frustrating for the boy. I did say to him that I've never known him be injured or even miss a day's training due to illness or anything else.
"It was a really good 14 minutes he had on his debut as well. I watched the game and was pleased with him.
"Every touch he had was impressive. He made important headers under his own bar, defended corners and started really well. It looked like he had been playing there for 10 years and not 10 minutes."