The 27-year-old Algerian international forward had wanted to move to the champions in January but City baulked at the £80 million fee Leicester demanded at the time.
Mahrez, though, said he did not wish to discuss the frustrations of the January transfer window and rather set his sights on what he can achieve at Manchester City.
"It's a club who wants to win this type of trophy. The Champions League is for big clubs and Manchester City are a big club," said Mahrez.
"They have everything to try to win the Champions League.
"It is a goal. Last season they lost in the quarter-final and I know they have the ambition to go further the next season.
"That's why I'm here, why I made the decision to come here, because I want to be part of this."
Mahrez, who was pivotal to Leicester's extraordinary title win in 2016 contributing 17 goals, said the size of the fee does not bother him or put pressure on him.
"The prices have been big in every country. This does not affect me," said Mahrez, who only cost Leicester £400,000 when they signed him in 2014.
Mahrez, who made 179 appearances for Leicester, scoring 48 times, admits there is a fine array of attacking talent already at City, including such as Belgian Kevin de Bruyne, Argentinian Sergio Aguero, German Leroy Sane and others, but he isn't losing any sleep over where he slots in.
"I never thought about this. I am very confident about myself."