Gatland has been in charge of the Lions since the 2013 tour of Australia, also leading the side during the 2017 tour of New Zealand and the South African tour in 2021.
"I have done my best for the Lions, but it is time to move on," Gatland said in his column in The Telegraph.
"A few weeks ago, I was asked by Nigel Walker, Wales' director of rugby, if I was interested in putting my name forward to be head coach for the next tour in Australia in 2025.
"I told him I was not going to put my name forward. I told Nigel that I would have no problem if any of my support staff were to be asked to be involved as I would see it as a great experience for them."
Gatland was also involved as assistant coach to Ian McGeechan (77) in the 2009 tour of South Africa, and is currently head coach of Wales who he led to the quarter-final stage of the Rugby World Cup in France this month.
The New Zealander also backed Farrell to be named as his successor.
"I think it is the opportunity now for someone else to be head coach and Andy Farrell would have my backing for the job.
"You cannot deny what Ireland have achieved as a nation over the last few years and you are starting to see the fruition of the alignment between the Irish provinces and the union. There is no doubt that Andy has done a fantastic job."
The next Lions starts with a match against Western Force at Perth Stadium on June 28th, 2025, with the series-opener against Australia at Brisbane's Lang Park on July 19th.
"If the next head coach wants to tap into my experiences from the last four tours, then I would still love to be involved in some way by passing on the knowledge and experience I have gained...," Gatland said.
"For the Lions, it is the least I can do."
