The Premier League club are preparing to finalise a £25 million deal with Liverpool for the 19-year-old Scotland international.
Doak, who joined Liverpool from Celtic in 2022 for £600,000, has been allowed to leave Anfield after making just ten appearances in three years.
According to reports, Liverpool will receive £20 million up front, with an additional £5 million paid in add-ons by Bournemouth.
The Scottish Sun claims that Celtic will receive a seven-figure sum from Liverpool due to a sell-on clause included in the original deal to sell Doak.
Doak will sign a five-year contract with Bournemouth, running until the summer of 2030.
After spending last season on loan with Middlesbrough, he now hopes to continue his development at the highest level.