Mahrez was strongly linked with a switch to the Etihad Stadium at the end of the January transfer window following an injury sustained by Leroy Sane, but the move fell through.
City has now broken the club's transfer record for the second time in 2018, the champion reported to have paid $NZD115 million for Mahrez, more than its previous landmark fee for Aymeric Laporte.
Laporte's $NZD111 million arrival from Athletic Bilbao eclipsed the $A98 million City paid to land Kevin De Bruyne from Wolfsburg in 2015.
"Riyad is a hugely talented player. He beats defenders and creates space," City's director of football Txiki Begiristain said.
"Over the past few years, he has established himself as one of the Premier League's most exciting players.
"We're sure he will bring additional attacking quality to our squad."