The Algeria global had his medical at City's training base today.
City are likely to spend more money before now and the transfer window closing on August 9.
The 27-year-old has penned a five-year contract with the Premier League champions.
He later said he had "regrets" over the dispute, during which the Professional Footballers' Association offered to be a mediator between club and player. "He beats defenders and creates space", City's director of football Txiki Begiristain said.
Sergio Ramos sends message to Cristiano Ronaldo over Juventus transfer
Other players targeted by Spanish tax authorities in recent years include Lionel Messi , Javier Mascherano and Luka Modric. Juventus president Andrea Agnelli was at Ronaldo's hotel in Greece on Tuesday as discussions continued over the move.
"Watching them from afar has been a pleasure".
"I am so pleased to have joined City, a side playing great football under Pep Guardiola", Mahrez told City's website.
"Riyad is a hugely talented player".
Mahrez has been linked with a move away from Leicester ever since their remarkable 2015-16 Premier League title win, scoring 12 goals and registering 11 assists in the most recent campaign. "We're sure he will bring additional attacking quality to our squad".
But the Premier League champions remained keen on Mahrez, who scored 13 goals in 41 appearances for Leicester last season.
'I think we can be successful over the coming years and I believe my own game can develop under Pep's management'. He will be welcomed back to King Power Stadium as both an opposition player and a friend of the Club.