Delaney said he was leaving to pursue "new opportunities" and intends to publish his third book and work on a new television show for Comedy Central.
He was appointed editor in September last year, replacing Julian Linley, who moved to the new role of creative director (TV) at Bauer Media in the same month.
The editor's role will be covered by Lucie Cave, executive editor, while Bauer looks for a permanent replacement. Cave will step up as acting editor of Heat from January.
She will report to Heat's managing director Sophie Wybrew-Bond, who said: "Lucie Cave is a huge talent who has become an invaluable member of the heat team over the past seven years, as a broadcaster, writer and senior editor."
In addition to her role at Heat, Cave presents a weekly entertainment show every Saturday on Heat Radio. She also ghostwrote the book "Jade Goody: My Autobiography".
Delaney said: "I have been honoured and privileged to edit such a great magazine and work with the best editorial team in the business.
"I have enjoyed every minute, but these new opportunities are too exciting to turn down. I wish Heat every success in the future and leave it in the supremely talented hands of Lucie Cave."