McGlynn departs with immediate effect after taking over at the helm last June.
First-team coach Gary Locke and player development manager Darren Murray will take interim charge of team affairs.
Hearts dropped to second bottom in the Scottish Premier League following their defeat to St Mirren.
McGlynn's departure comes after the loss to St Mirren saw Hearts slip to second bottom of the Scottish Premier League.
He told Hearts News: "I was very grateful to be given the chance to become the Hearts manager as it was my dream job.
"It was an honour and privilege to serve the club in this capacity and I thoroughly enjoyed working with the players, who have been top professionals.
"It is unfortunate that things didn't turn out the way I wanted them to and I am gutted about that.
"I am a worker and want to get back into football as quickly as possible.
"I don't think I could have done any more, but the league table doesn't lie and I know it is a results-driven business.
"We had a lot of difficult circumstances to deal with and they have taken their toll in the end, but no-one will be more delighted than me if the team can go on and win the League Cup."
McGlynn added: "I would like to thank all the backroom staff - the physios, medical staff and video analysis department - also the club's media department and everyone at Tynecastle for being good fellow workmates."
Locke and Murray will be in charge for Saturday's visit of Motherwell, as the club begin the process of finding a permanent manager.
According to the Jambos website, club chiefs are "planning to start discussions with candidates as soon as possible".
A Hearts spokesperson said: "When John came to the club, Hearts was embarking on a transitional phase in the club's history.
"He began that important period of change and it is now imperative we find the right man to take the transition forward.
"The over-riding factor in this decision was the long-term well-being of Heart of Midlothian Football Club.
"We would like to thank John for his tireless efforts as manager of Hearts and wish him well with his career. He will be welcomed back to Tynecastle as guest of the club at any time."
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