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.
Mahrez was given permission by the Foxes to miss their pre-season trip to France on Monday to conclude the deal.
"I am so pleased to have joined City, a side playing great football under Pep Guardiola", Mahrez said in a club statement.
Riyad's progress with Leicester City also saw him firmly establish himself as a key member of the Algerian national team, with whom he played in the 2014 FIFA World Cup Finals and both the 2015 and 2017 Africa Cup of Nations. "Pep is committed to playing attacking football, which is a flawless for me, and City's performances last season were outstanding", he said on the club's official website. "They're redefining the English game and I wanted to be a part of it", Mahrez said on his new club's website.
Meanwhile, NAIJ.com previously had reported that Manchester City are reportedly close to landing Leicester City star Riyad Mahrez this summer.
"Riyad is a hugely talented player".
Oblak has established himself as one of the world's very best goalkeepers during his four years with Atlético Madrid and the Slovenian worldwide would represent a major summer coup for Liverpool, if a deal can be struck.