Winger Bentley was Tottenham's record signing when he arrived from Blackburn for 17 million pounds in 2008 but failed to make any impact at White Hart Lane and has spent loan spells at Birmingham City, West Ham United and Russia's FC Rostov.
The 28-year-old, who has seven England caps, could make his debut against boyhood club Arsenal in the FA Cup fifth round on Saturday, mid-table Blackburn said in a statement.
Defender Rekik, 18, made his Premier League debut for City in December and has also joined Rovers until the end of the season.
Rekik, who plays for the Netherlands Under-19 side, spent the end of last season on loan to Portsmouth.
"I'm happy to say that I'm going on loan to Blackburn Rovers and be part of the team," Rekik said on Twitter.
"Hope to win many games and learn for my future at Man City."