The 18-year-old, who can play at centre-half of left-back, initially revealed the news via his Twitter account and Rovers have now confirmed the deal on their official website.
"Happy to say that I'm going on loan to Blackburn Rovers and be part of the team. Hope to win many games and learn for my future at Man City," said the Holland U19 international.
Rekik, who joined City's academy from Dutch side Feyenoord at the start of the 2011/12 season, has made three appearances for Roberto Mancini's side, twice in the Carling Cup and once in the Premier League, against Reading in December last year.
He spent a month on loan at Portsmouth last campaign, playing eight games.
Rekik has joined Blackburn in time to be included in their squad for Saturday's FA Cup tie against Arsenal.