The Netherlands international, 22, had a spell
on loan with the Cherries last season and scored three goals in 12 games before being
recalled.
The fee, reported to be £20m, breaks Bournemouth's
previous record - the £15m paid to Liverpool for winger Jordon Ibe
in July 2016.
Ake has signed a long-term deal and is the
Cherries' third summer signing.
England striker Jermain
Defoe signed on Thursday from Sunderland and Bosnia goalkeeper Asmir
Begovic arrived from Chelsea in May.
Ake joined Chelsea in 2012 and made 17
appearances for the Stamford Bridge side. He spent the 2015-16 season on loan
at Watford in the Premier League.
"I had a great time last season so I'm
really happy to be back," said Ake. "The fans haven't seen the best
of me yet."
Ake, who moved to Chelsea from Dutch side
Feyenoord aged 16, has two caps for Netherlands and made his debut in a
friendly against Morocco in June.
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."
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