The 19-year-old made his debut for City against Preston North End in the EFL Cup in September 2019 and has gone on to make a further eight appearances across all competitions for Pep Guardiola's side.
Harwood-Bellis will spend the rest of the 2020-2021 campaign with Rovers, who are eighth in the Championship.
His move means it is unlikely fellow central defender Eric Garcia will be allowed to join LaLiga giants Barcelona.
There had been suggestions Garcia would return to his boyhood club before the close of the mid-season transfer window on Monday, but Guardiola will want to ensure he has adequate cover for the heart of his defence in the second half of the season.
The 20-year-old's contract expires at the end of this season and it appears he will have to wait until then to rejoin Barca.