Chief executive officer Simon Wilson is also leaving Edgeley Park after six years while long-serving keeper Ben Hinchliffe departs after 10 years and Challinor added: “It feels a little like the end of an era (with) the club entering a new phase with new people coming in.
“For me, it feels like the right time for all parties to look at what comes next, while leaving immensely proud of everything we’ve achieved together.”
Challinor – who was the English Football League’s fifth longest-serving manager – has been linked with the vacant Blackburn Rovers job, but said he planned to spend some time away with his family.
In a message to fans, Challinor, who had signed a new long-term deal only last year, added: “Your backing has been incredible and I’m sure that will continue.
“From game one, when 5,000 of you travelled to Bolton, to game 268 and 15,000 at Wembley for the third time in four years, your support never wavered. Annoyingly, we couldn’t reward that with a win, but that moment will come.
“I hope we can all reflect positively on the experiences and emotions we’ve shared together over these years, mostly good, with a few painful moments along the way.
“I’ll be back at Edgeley Park as a watcher and a supporter, and hopefully I’ll get the opportunity to say thank you and goodbye properly in person.”
Stockport, who have finished third in League One the past two seasons only to fall short in the play-offs, said the decision had been made mutually after “long and constructive discussions”.
Hatters owner Mark Stott told the club website, external: “Since buying the club, there have been a few County legends mentioned to me, and in management there is obviously Jim Gannon and Danny Bergara. Dave Challinor definitely now joins that list.
“From the day Simon [Wilson] and I first met Dave, we knew we had found the right person to kick-start our vision for the club. His track record spoke for itself, but it was Dave’s human qualities that gave us complete confidence he was the man for the job.
“Five years on, the achievements speak for themselves. We have reached at least the play-offs every season, won two league titles and broken so many records along the way. Dave has played a huge role in transforming the club and helping us build foundations for the future.”