The 17-year-old went on loan to Portsmouth in March and won admiration for his performances despite the club's subsequent relegation to League One.
"It was a very easy decision to make, City is a great club with a great future for me," said Rekik. "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% and I'm happy to be back and playing. I'm delighted to be staying at City."