Ms Burrow has been deputy editor of the magazine since 2005 and has been acting editor for the past seven months since previous incumbent Jane Johnson was appointed editorial director for Closer and stablemate First.
Jane Johnson has since agreed to leave Emap to join the News of the World.
Emap was last week given the go-ahead to launch Closer Radio after 4 Digital Group was awarded the licence to operate the UK’s second national commercial DAB multiplex.
Sophie Wybrew-Bond, deputy MD of Emap Entertainment, said: "Lisa was simply the best person for the job given her broad experience and understanding of Closer's brand values and its unrivalled standard of editorial that mixes celebrity news, real life stories and lifestyle advice."
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