The Premier League champions sanctioned the move because Ake wants regular football, but they insisted on a buy-back clause being inserted in the deal.
The exact details of the clause have yet to be revealed but it raises the prospect Ake could still return to Stamford Bridge in the future.
Blues boss Antonio Conte was so impressed with the 22-year-old after his return from a loan spell with the Cherries that he trusted him to start the FA Cup Final.
Ake has decided to jump ship and now becomes Bournemouth’s record signing and he said: “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 need to work on.
“With the help of the manager here I know I can keep improving and become a better player.”
Ake made his Premier League debut for Chelsea as a 17-year-old after joining them from Feyenoord’s youth set-up, and went on to be named their Young Player of the Year.
But he found first-team football hard to come by and was loaned out to Reading and Watford before spending the first six months of last season at Bournemouth.
Cherries boss Eddie Howe, who has already snapped up Jermain Defoe and is planning further signings, said: “I am delighted. He is someone we know all about.
“Nathan is an outstanding young player with a fantastic attitude and a great desire to learn and develop.
“He has a very bright future ahead of him and I’m very pleased to say that future is here.”
Ake’s signing means Bournemouth could now end their interest in former Chelsea skipper John Terry, who has offers on the table from other clubs including Aston Villa and Birmingham.
