Solanke scored just one goal in 27 appearances for Liverpool after joining the club on a free transfer from Chelsea in 2017. He has not featured for the club this season.
Reports also said that Liverpool right back Nathaniel Clyne could follow Solanke to the Vitality Stadium, with the club short of options in defence after injuries to captain Simon Francis and Adam Smith.
The 21-year-old is keen to play first-team football, having left Chelsea for exactly that same reason and with little chance of displacing the trio of Roberto Firmino, Sadio Mane or Mohamed Salah in the near future has made a decision to look elsewhere.
In terms of arrivals, Jurgen Klopp indicated last month that he was not expecting to sign anyone: "I'm very happy with what I've got".
"I am looking forward to seeing him pull on an AFC Bournemouth shirt and am confident he can help us build on a record-breaking first half of the season".
The worry amongst Bournemouth fans will be that the arrival of Solanke could pave the way for Callum Wilson to leave the club, with Chelsea known to be massive admirers of the England worldwide.
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Ramsey is now playing for his future away from the Emirates Stadium amid interest from some of Europe's biggest clubs. At the moment he's working with us and I think yes [he's going to stay]'. 'I want this focus when he's playing.
Solanke was on the verge of a move to Crystal Palace earlier this week, only for the move to break down after a medical.
"Bournemouth made a good offer, to be honest".
"He has done very well for England at various age groups, has a huge amount of potential and I'm really excited about working with him".
"When I came in, he played like what I felt was each game".
Clyne is in a similar position in having seen his first-team chances drastically reduced due to the form of Trent Alexander-Arnold and Joe Gomez. That opened the window for Bournemouth to move and Eddie Howe has now splashed the cash to bring in the English youngster.
"Dominic will miss most of January", said Howe, after his side's 3-1 FA Cup third round defeat by Brighton.
"[Gomez is] getting better, but not yet involved", the Liverpool manager said.