The 18-year-old Dutchman has made one Premier League appearance this term but will join the Championship club on a deal that runs until the end of the season
The 18-year-old's representative met with officials from the Championship club on Thursday morning in order to finalise the temporary move.
Rekik, a Netherlands Under-19 international, was loaned out to Portsmouth last season and has make just one Premier League appearance this term - City's 1-0 victory over Reading on December 22.
"Happy to say that I'm going on loan to Blackburn Rovers and be part of the team," Rekik posted on Twitter.
"Hope to win many games and learn for my future at Man City."