The 22-year-old spent the first half of last season on loan at the Vitality Stadium, scoring three goals in 10 Premier League appearances before being recalled by Chelsea.
The likes of West Bromwich Albion, Newcastle United, Southampton and West Ham United were all thought to be interested in the Dutchman, but numerous reports claim that Bournemouth have won the race for his signature.
The defender is expected to sign a five-year contract with the Cherries after a deal was agreed in principle between the two clubs, and the move could be completed in the next 48 hours.
However, the contract will include a buy-back clause for Chelsea, who remain keen admirers of Ake despite his relative lack of game time at Stamford Bridge.
Bournemouth's current record transfer saw Jordon Ibe join from Liverpool for £15m last summer.