The highly-rated youngster joins Villa for an undisclosed fee, signing a two-and-a-half-year contract that will keep him at the club until 2019.
Bedeau broke into the first team at Bury earlier this season, making seven League One appearances for the Shakers since his debut in November.
"This is such a massive opportunity for me at such a young age. I'm looking forward to taking that opportunity and developing even more at such a big club," he told the club's official website.
"I'll always be grateful to Bury for giving me a chance so I would like to say thank you to them and wish them all the best for the rest of the season. I can't wait to get started at Aston Villa."
Bedeau becomes Villa's fifth signing of a busy transfer window.