Ake spent the first half of last season on loan with the Cherries, but after impressing at the Vitality Stadium, he was recalled by Blues head coach Antonio Conte.
However, he made just five appearances in all competitions and after a bid reportedly in the region of £20m was made, Chelsea decided to part ways with their academy graduate and he has signed a long-term deal with the south coast outfit.
The 22-year-old told the club's official website: "I had a great time here last season so I'm really happy to be back. It's an exciting challenge. Chelsea is a great club and I learned so much there but this is a new step and the right place for me to develop even more.
"The fans haven't seen the best of me yet. I always set the bar high so I know there is a lot of things I still have to work on.
"With the help of the manager here I know I can keep improving and become a better player."
Ake leaves Stamford Bridge having made a total of 17 appearances in all competitions, although he only made two starts in the Premier League.