Klopp predicts limited transfer activity for Reds
The two clubs had discussed an extension because the coronavirus pandemic delayed the end of the 2019-2020 campaign beyond the original expiration date of the winger's stay.
Wales international Wilson has been a key contributor for Bournemouth, scoring seven times in 23 Premier League appearances.
Following Monday's extension, the 23-year-old will bid to help Eddie Howe's side move out of the relegation zone over the last nine games of the season.
Bournemouth sits 18th in the table as part of a competitive battle against the drop, with only four points separating Brighton and Hove Albion in 15th and Aston Villa in 19th.
The Cherries are scheduled to return to action with a home match against Crystal Palace on 20 June.