Bournemouth and Chelsea have agreed a 20m deal for the 22-year-old Dutchman.
Ake will join Jermain Defoe who completed a move from relegated Sunderland.
“I had a great time here last season so I’m really happy to be back,” Aké told Bournemouth’s website. “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.”