Financial details were not revealed, but British media reported the Premier League champions have accepted an offer from the Saudi side worth 35 million euros ($38.53 million) plus five million in add-ons.
"I have had five unforgettable years with this football club, working with unbelievable players, fantastic supporters, and the best manager in the world.
"Manchester City will forever be a huge and happy part of my life."
Mahrez scored 78 goals and made 59 assists in 236 appearances in all competitions with City, and won 11 trophies at the club, including five league titles following his move from Leicester City in 2018.
The Algerian winger saw his role for Pep Guardiola's side reduced last season, scoring 15 goals in 47 games, but missing out on action in the FA Cup and Champions League finals as City won their historic treble.
Last year Mahrez renewed his contract until 2025.
City could also part with another midfielder as Portuguese international Bernardo Silva has been linked with a move to Saudi Arabia with Al-Hilal, according to British media reports.