The Algeria winger was officially announced as a Man City player on Tuesday, penning a five-year contract at the Etihad Stadium.
Mahrez, who joined the Foxes from Le Havre for £400,000 in 2014, was instrumental as the modest East Midlands club won the Premier League title in 2016.
"To all Leicester fans, we have made some amazing memories and history together," Mahrez wrote on his Twitter account.
"Winning the Premiership against all odds was just something else and none of this would have been possible without your extraordinary support for me and the team.
"I want to thank all of you for welcoming me to the club right from the start and continuing to give me the belief and encouragement to achieve what we have together.
"I would also like to thank my teammates, staff and everyone at the club who have become a big part of my life in the last few years.
"Now it's time for me to move on and try to build on what I have developed here, but I will always remember my time at the club with great joy and pride. Thank you, Thank you, Thank you."
Mahrez scored 13 goals in 41 appearances for Leicester last term.