"I had a great time here last season so I'm really happy to be back," Ake told Bournemouth's website (www.afcb.co.uk) of a move British media reported to be for a fee of 20 million pounds.
"It's an exciting challenge... this is a new step and the right place for me to develop even more. With the help of the manager here I know I can keep improving and become a better player."
Ake previously completed loan spells at Watford and Championship side Reading.
"I am delighted that we have completed the signing of Nathan on a permanent basis," Bournemouth manager Eddie Howe said.
"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."
(Reporting by Aditi Prakash in Bengaluru)
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