Julian Linley, editor of and a former deputy editor of Heat, has agreed to become acting editor of the magazine and will work alongside Frith on the handover.
Linley will continue to edit heatworld.com and will remain as acting editor until Bauer confirms Frith's successor, when Finley intends to return to his post.
Frith started his career at Emap's Smash Hits in 1990 and in 1994, at the age of 23, he was appointed editor before leaving for Sky Magazine in 1996.
In 1997, Frith joined a project team at Emap to work on the launch of Heat, starting as deputy editor.
Heat launched in 1999 as a unisex entertainment title, but it was reinvented in 2000 at the time of Frith's appointment into a groundbreaking celebrity women's weekly that has gone on to define the celebrity era.
The move comes after two major events to affect Heat, the first coming when the magazine generated scores of complaints to the Press Complaints Committee over a sticker featuring glamour model Jordan's son Harvey.
The sticker, which mocked Harvey's medical condition, forced Frith and Emap into an embarrassing public apology and tarnished the brand's image.
Shortly after this, Emap's consumer magazines, including Heat, were sold to German publisher H Bauer in a £1.1bn deal.
Marcus Rich, group managing director of BCM's London lifestyle brands, said: "While we are obviously extremely sorry to lose Mark, he leaves a great team and a strong cross-platform brand that will continue to excite the Heat community.
"As a former deputy editor of Heat, Julian has a huge heritage with the brand, is extremely experienced and I have no doubt will manage a smooth transition.
Frith said: "Taking Heat from sales of 65,000 a week to over half-a-million has been an exhilarating experience. The Heat team is truly exceptional and I wish them all the best for the future."
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