The 22-year-old winger has come through the ranks at Liverpool and last season was on loan at Derby County, scoring 15 goals in 40 appearances to help the Rams reach the Championship playoff final.
Wilson is AFC Bournemouth's fifth arrival of the summer, following Lloyd Kelly, Jack Stacey, Philip Billing and Arnaut Danjuma.
"It's great to be here, great to finally get everything sorted and I can't wait to meet all the staff and the lads,” Wilson told afcbTV.
"When Liverpool informed me it was a possibility to come here I was keen to get it sorted. I want to play Premier League football and with a great team like Bournemouth.
"With the style of play that Bournemouth are likely to play I feel that I can fit right in and help the team a lot.”
AFC Bournemouth open their 2019/20 campaign at home to Sheffield United on Saturday 10 August.