City have always been in pursuit of Mahrez, having seen a cash-plus-player offer of £65m for the 27-year-old rejected in January, with Leicester demanding £80m to let him go in the middle of the season.
Mahrez was the subject of four failed bids from Manchester City in the mid-season transfer window and, after a move to the Etihad did not materialise he missed training for over a week, with the Algeria worldwide forced to deny going AWOL.
According to The Mirror (Transfer Live blog, 19:18pm, Saturday, July 7, 2018), Roberts is leading to Leicester from Premier League champions City in a £10 million deal.
"Riyad leaves with the best wishes of everybody who has worked with him at Leicester City Football Club".
It is understood that Mahrez has been given permission by Leicester to stay at home and continue his own personal training programme.
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The 27-year-old Algerian is the Blues' first signing since they won the Premier League title.
City's director of football Txiki Begiristain added: "Riyad is a hugely talented player".
Pep Guardiola is a long-term admirer of Mahrez, and will have been impressed with his dedication in the second half of the season at Leicester despite coming close to an exit in the January window.
He later said he had "regrets" over the dispute, during which the Professional Footballers' Association offered to be a mediator between club and player.
"Watching them from afar has been a pleasure".
Mahrez's experience of winning the Premier League will certainly have left him hungry for more success, and he now has the chance to achieve that once more under the stewardship of Pep Guardiola. "He will be welcomed back to King Power Stadium as both an opposition player and a friend of the club".