Ayre, who has been at Anfield since 2007, announced back in March that he was to leave his role as CEO, and was initially expected to depart at the end of the 2016-17 season.
However, he will now leave his post on Merseyside to become general manager of 2. Bundesliga side 1860 Munich at a later date, which is yet to be announced.
Liverpool continue their search for Ayre's replacement and aim to fill the position in the summer as always planned.
Meanwhile, as part of structural reform at the club, commercial director Billy Hogan has been promoted to managing director and chief commercial officer, while Andy Hughes is now chief operating officer.
In November, Liverpool announced the promotion of Michael Edwards to become the club's first ever sporting director.
Speaking on behalf of Liverpool's owners, Fenway Sports Group, president Mike Gordon said in a statement: "Although this transition has been nearly a year in the making, today is still a difficult day -- we are officially saying goodbye to Ian.
"On behalf of John [W. Henry] and Tom [Werner], I would like to place on record the outstanding contribution Ian has made to Liverpool Football Club over the past 10 years.
"It goes without saying that his leadership of LFC has been instrumental to the club's progress under our ownership. It is a measure of his character and his commitment to LFC that we have been able to collectively plan and execute such a gradual, natural transition.
"On both a professional and personal level, he will be missed."
On Ayre's replacement, Gordon said: "We are very pleased with the search progress and fully expect to have our new CEO in position by our original deadline of the summer 2017.
"We are quite confident that LFC will have the right structure and the best people operating within that structure to fill the lofty ambitions of LFC and its supporters."
Ayre said: "There is no greater professional satisfaction for me than to leave Liverpool Football Club in much improved health throughout than when I joined the club in 2007.
"This has always been more than just a job for me because of the emotional connection I have with the place. So, the only yardstick that has ever mattered, for every decision I have taken here, is whether or not it is in the best interests of Liverpool Football Club.
"My journey here over the last decade has been a rich mix of challenges and opportunities, a journey only made possible by the outstanding people I have had the honour to work with along the way both inside and outside the club.
"As the club transitions to its next chapter, I made clear some time back that I felt that 2017 was the right time to step aside.
"As the club's new structure starts to unfold, this is a natural point for me to say goodbye to the role of chief executive and to many friends, but my love and support for this great football club will continue as it has my whole life."
The boyhood Liverpool fan joined the club in 2007 as commercial director before he was promoted to managing director in 2011 and then CEO in 2013.