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The paranormal series - created by Neil Jones, David Allison and Chris Parker - will return for a second run later this year.
Mead, who won BBC talent show Any Dream Will Do in 2007, will play a character named Scott in one episode.
"When the role in Bedlam came up I was really excited at the chance to be involved, and star alongside such a great cast in a fresh and original psychological drama," said the West End star.
"It's completely different from anything else I've done before. And while I can't give too much away about my character Scott, I think it's safe to say that the episode I'm in is genuinely scary - I'm really looking forward to seeing it back."
Last year, Mead made his television acting debut in an episode of Casualty.
The second series of Bedlam will feature a revamped regular cast, led by former EastEnders star Lacey Turner.
The Cafe's Jack Roth, Secret Diary of a Call Girl's Gemma Chan and Nikesh Patel will also join original stars Hugo Speer and Charlotte Salt in the new episodes.
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