She replaces Nigel Horne, who left the magazine in April after less than a year in the post.
Hudson joined the BBC in 1999 and was launch editor of Eve for the first 18 months of its life until earlier this year. Most recently, she was editorial director of new product development at BBC Magazines. She takes up her new role on Monday.
Hudson's career in publishing also includes a spell at Dennis Publishing, during which time she was launch editor of Maxim in the UK, was involved in the launch of the US version and oversaw the creation of Stuff.
Hudson is credited with having launched Ministry magazine for UK clubbing brand Ministry of Sound and was editor of New Woman magazine at Emap when the title's ABC circulation grew for seven successive periods.
Her first notable success was as editor of NatMags' Company magazine, which she is said to have rescued from the brink of closure.
Ashley Munday, publishing director of the Radio Times, said: "Gill is one of the industry's best-known and most respected talents, and has already had an exceptional editorial career. She has a passion for magazines that is hard to resist and will now help to take Radio Times to even greater success as we lead the way in the multichannel listings market."
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