Ayre, 52, joined the five-times European champions in 2007 as commercial director. He moved on to the board of directors two years later before being promoted to managing director in 2011 and CEO in 2013.
He has presided over what Liverpool described as a radical modernisation during which he brought stability following the Fenway Sports Group takeover in October 2010.
"Under his leadership we have seen Liverpool transform from a club that was on the brink of bankruptcy to one which today enjoys strong financial and operational health," principal owner John W Henry, chairman Tom Werner and president Mike Gordon said in a statement.
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"Stability is a commodity often under-valued in sporting organisations but it has been a fundamental hallmark of Ian's time in charge. Liverpool will reap the benefits of his outstanding work for many years to come.
"There will continue to be important milestones for Liverpool over the next 15 months, not least the completion of the redevelopment at Anfield stadium, and we are grateful Ian will continue his leadership through to May 2017," read the statement.
The owners tried on several occasions to persuade Ayre to change his mind and he has announced his decision now to give the club time to find a replacement.
"If becoming chief executive of Liverpool Football Club was the greatest honour of my professional life, then deciding to step down at the end of my current contract is by far the most difficult," said Ayre.
"Having been brought up in the shadow of Anfield, I have found it the most profound privilege to serve the club I have supported all my life.
"I believe the end of next season is the right time to pass the CEO baton on to a new person who will take on the challenges and opportunities with a fresh enthusiasm and vigour."
(Writing by Ken Ferris; Editing by Tony Jimenez)
