The news came following their 4-2 defeat to Kidsgrove Athletic on Monday afternoon.
Baker took charge of the Blues for the third time in June 2017, having first managed the club in a highly successful spell from 1986-94. During that time, he led them into the Northern Premier League and to the FA Trophy final in 1990.
His second spell at Harrison Park in 2011 came either side of stints at Crewe Alexandra.
Baker led Leek to a play-off final in 2018/19 and took them top of the table in 2019/20 and 2020/21, with both seasons curtailed due to the Covid-19 pandemic.
They finished second in the Pitching In NPL West Division last season - 14 points behind champions Macclesfield - before losing out to Runcorn Linnets in the play-offs.
They currently sit eighth in the NPL West Division league table, having picked up seven points from their opening five games.
A club statement confirmed that Baker had the intention to step away from his role regardless of their result against Kidsgrove.
It is unclear whether his successor will be in place before Saturday's home game against Grimsby Borough in the FA Cup first qualifying round.
Chairman Jon Eeles said: "Neil has legendary status at the club and there will be enormous shoes to fill going forward.
"I completely respect his decision and the professional way he has conducted himself today and in the past.
"He will always be welcome at the club, in whatever capacity he wants to watch a game, and I wish him and his family all the very best for the future."
Photo credit: Leek Town