The centre-back, who spent time on loan at Portsmouth last season, has set his sights on a place in the Blues' first-team squad after committing his future to the club
The 18-year-old, who can play at both centre-back and left-back, joined the club from Feyenoord in 2011 and made two appearances for Roberto Mancini's side before making a further eight on-loan at Portsmouth in the Championship at the end of the season.
Rekik, who has missed three months of the current campaign with a back injury, has targeted a spot in the City first team.
"It was a very easy decision to make, City is a great club with a great future for me," Rekik told the club's official website.
"I can develop as a player and a person at this club and that's why I decided to stay.
"It feels like family inside at City, everybody is nice and they all speak to me so it was very easy for me to settle in. It definitely gives you a boost in confidence to be given a contract considering that we won the league last year.
"That was a great experience for me and I really hope to be a big player for City one day. If I train against those players it's great for me, it's fantastic to play against these great players and it can only help me learn.
"I've been out for three months with a back injury but I feel 100 per cent and I'm happy to be back and playing. I'm delighted to be staying at City."