Solanke's arrival was the first of two moves from Anfield to the Vitality Stadium on Friday, with Reds defender Nathaniel Clyne also joining on loan until the end of the season.
It is expected that Solanke's switch to the south-coast will pave the way for Bournemouth's veteran striker Jermain Defoe to join Rangers on an 18-month loan.
Solanke began his career at Chelsea, playing a season on loan at Dutch side Vitesse Arnhem before joining Liverpool in 2017.
He made 27 appearances for Liverpool in his first season but has not featured for Jurgen Klopp's side in the current campaign.
The 21-year-old is keen to play first-team football, having left Chelsea for that reason but had little chance of displacing the trio of Roberto Firmino, Sadio Mane or Mohamed Salah at Liverpool.
"I think the club (Bournemouth) is going somewhere," Solanke told afcbTV. "Over the past few years, they have been really good in the Premier League and had some good positional finishes as well. I think it's a good club to be at, especially for someone of my age."
Bournemouth manager Eddie Howe said: "Dominic is technically gifted, very athletic and has the physical profile that will give us something different in our front line."
Clyne, 27, is in a similar position to Solanke having seen his first-team chances reduced due to the form of Liverpool defenders Trent Alexander-Arnold and Joe Gomez.
The right-back has played just five times this season and managed only a similar number in the previous campaign because of a back problem.
"I'm really excited by this opportunity. It's a great chance for me to come and play football," Clyne said.
"I've spoken to the manager and we've talked about what we can achieve for the remainder of the season. It's a great club with a great story. I can't wait to get going."