The highly-rated 18-year-old joins Rovers from the Premier League champions on a youth loan until the end of the season.
A versatile defender, who is equally comfortable both at left-back and centre half, Rekik started his career with Dutch giants Feyenoord, before securing a summer switch to Manchester City in July 2011.
Rekik made his City debut two months later in the League Cup, before making a loan move to Portsmouth where he played under Rovers boss Michael Appleton until the end of the 2011-12 season, making eight appearances.
The Dutch youth international made his Premier League debut earlier this season, starting in City’s 1-0 win over Reading in December, and is tipped to have a bright future at the Etihad Stadium.
The Rekik deal has been completed in time for inclusion in tomorrow's squad for the FA Cup tie with Arsenal.