Cave was previously acting editor at the title and has spent over seven years at Heat, joining in 2003 as a freelance news reporter from a broadcasting role at Trouble TV.
She was promoted to the position of executive editor in 2008 and stepped up as acting editor earlier this year.
Sophie Wybrew-Bond, managing director of Bauer Entertainment for Closer, Empire and Heat, said: "Embodying the heart and soul of heat, Lucie has an instinctive understanding of the brand and this has led her to do a great job as acting editor.
"I have no doubt she will lead the heat team successfully forward and continue to deliver the hottest and most relevant celebrity news with heat’s usual cheeky humour."
During her time at the title Cave has co-hosted ITV2's National Television Awards coverage and has appeared on ITV2’s structured reality show 'The Only Way is Essex'. She was also co-writer for an episode of Channel 4 soap 'Hollyoaks', with Jeremy Mark, Heat's deputy editor.
Cave said: "It's a huge honour to be appointed editor and I'm absolutely thrilled to be leading such a fantastic team. Heat is the definitive guide to celebrity news and entertainment and while it has many imitators, there’s no magazine quite like it.
"To continue to achieve stand out, break exclusives and make readers laugh – we're constantly raising the bar with new sections to the magazine, exclusive celebrity shoots, PR stunts and celebrity fashion."
In the latest figures from the Audit Bureau of Circulation (ABC) last month, Heat reported the steepest circulation drop in the celebrity weekly sector.
The title had an average circulation of 326,677 in the first six months of 2011, down 21.7% year on year and 11.7% period on period.
Cave replaces previous editor Sam Delaney who left the title in December 2010.