The 27-year-old will face competition from the likes of Leroy Sane, Raheem Sterling and Bernardo Silva for a place in Pep Guardiola's side, but he has no problem with fighting for his spot in the starting lineup.
"I haven't talked about my precise position with the manager yet, but City wanted me and that means a lot," Mahrez told reporters at this official unveiling.
"The price tag doesn't affect me – fees for players have got very big in the last couple of years. I am very happy to be here and will try to give my best for the club. I thought what City did last year was amazing, it was unbelievable to break all those Premier League records, but I am confident about myself.
"I want to help this team improve and I believe that is what the manager wants. Players at top clubs always have to face competition for places, it is normal for big clubs to have a lot of great players and City are a big club with a big manager."
Mahrez's first appearance for his new club could come next Saturday when they face Borussia Dortmund in the International Champions Cup.