Linley is editor of Heat's website and has been acting Heat editor for the past few months, in a handover period that started when Frith handed in his notice in February.
Frith left this month after 10 years as editor, to write a book.
Linley will now become editorial director of , in addition to his responsibilities as Heat editor.
David Davies, managing director of Heat, said: "There isn't another brand to match Heat's presence or potential in the celebrity space, which is why this job attracted a stellar cast of applicants.
"Julian's long heritage with the brand means he brings an unrivalled insight and understanding into the Heat consumer.
"This, combined with an instinct for agenda-setting celebrity editorial, makes him the perfect man to appoint as editor."
Linley spent five years as deputy editor of Heat from May 2000, moving on to work on the planning of sister title First and edit it from launch in 2006. He then moved to oversee the launch of HeatWorld.com in May 2007.
He said: "There is no better job than being the editor of Heat. Ever since I first joined the magazine for its relaunch in 2000 I have loved coming to work each day -- there's just something about Heat that's special."
Under Frith, Heat ran into a row last year over a sticker it gave away featured Jordan's disabled son Harvey with the text "Harvey wants to eat me!". It lead to 56 complaints being made to the Press Complaints Commission.
As Linley takes over, Heat's circulation is at 533,304, according to ABC magazine figures for July-December 2007. This is down 4.5% period on period and 11% year on year.
In addition to the magazine, the Heat brand covers a mobile version of HeatWorld and the website, which has 430,000 unique users. It also includes the Heat digital radio station, which has a weekly reach of 446,000 listeners.
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