"Konate will leave with our gratitude and appreciation for the contribution he made and everyone at the club wishes him all the best for the future," the club wrote in a statement on Sunday.
Konate was a key cog in the team's charge to Premier League glory in the 2024-2025 season. He also won two League Cups and the FA Cup during his time at Anfield.
But the 27-year-old French international's form was shaky during parts of the recently concluded season, when "the Reds" had to settle for fifth place.
He is now leaving on a free transfer, which means Liverpool will not receive any transfer fee for him.