The 18-year-old rejected the offer of a contract extension at Stamford Bridge to join the Cherries.
"I've been looking forward to coming here for a few weeks now," Muleba told Bournemouth's official website.
"I've seen that the players in the development squad get opportunities here and the chance to train with the first team, which was important to me.
"It's always difficult to leave home, because I'm from London, and what you know, but in terms of football it was quite an easy decision."
Muleba will link up with Bournemouth's development squad.