The 27-year-old, who joins for a club-record £60m, has signed a five-year contract at the Etihad Stadium.
Mahrez becomes Pep Guardiola's first major signing of the summer following a season in which the Citizens broke several records en route to the Premier League title.
"I am so pleased to have joined City, a side playing great football under Pep Guardiola," the Algeria international told the official club website.
"Watching them from afar has been a pleasure. Pep is committed to playing attacking football, which is a perfect for me, and City's performances last season were outstanding. They're redefining the English game and I wanted to be a part of it.
"I think we can be successful over the coming years and I believe my own game can develop under Pep's management."
Mahrez joined Leicester from Le Havre for £400,000 in 2014, and was named the PFA Players' Player of the Year during their surprise Premier League title triumph two seasons ago.