The Algeria worldwide had his medical at City's training base today.
Mahrez scored 13 goals in 41 appearances for Leicester last season and will become City's record signing ahead of defender Aymeric Laporte, who signed from Athletic Bilbao for £57m in January if the deal happens.
It is understood that Mahrez has been given permission by Leicester to stay at home and continue his own personal training programme.
The two clubs have agreed a fee of £60m for the 27-year-old and talks have now been completed between the two sides, with Mahrez due in the north west for a medical at the start of next week.
"I am so pleased to have joined City, a side playing great football under Pep Guardiola", Mahrez told the club's official website.
Egypt denies reports that cockpit fire likely caused 2016 Egypt Air crash
French investigators and the families of the French victims have deplored a lack of cooperation from the Egyptian authorities. It is unusual for investigators to comment publicly on a case being led by their counterparts in another country.
City's director of football Txiki Begiristain added: "Riyad is a hugely talented player".
"Watching them from afar has been a pleasure". They're redefining the English game and I wanted to be a part of it. "Over the past few years, he has established himself as one of the Premier League's most exciting players".
City cruised to the Premier League title, becoming the first team to hit the 100-point barrier since the Premier League was founded in 1992.
Despite going AWOL for 10 days at the beginning of February, Mahrez put in some fantastic performances for Leicester during the second half of the season.
Interestingly, the Algerian was back in Leicester's good books as he netted four more goals for the Foxes, taking his total goals to 39 goals from 139 top flight games for the King Power dwellers.