Minamino ended his two-and-a-half year stay at Anfield on Tuesday, signing a four-year contract with the French giants.
The Japanese international came to England with a big reputation but struggled to break into Klopp's starting eleven, spending time on loan at Southampton in the second half of the 2020/2021 campaign.
In all, Minamino made 55 appearances for Liverpool, scoring 14 goals.
Minamino won the Premier League, FA Cup and Carabao Cup with Liverpool.
“It’s hard to see Taki go, but it’s a great move for him and one he thoroughly deserves," Klopp told Liverpool's official website.
“An amazing professional; super, talented player. As a person, he is full of warmth and makes everyone feel positive. A manager’s dream, to be honest.
“I’m sure there will be those who think it didn’t quite work out. Those who think this are wrong. I don’t accept that.
“His contribution far outweighs the opportunities we were able to give, in terms of starting matches. He made us better each and every day he was with us – not just in the games he played in but every single session in training. Perfect attitude, winner’s mentality.
“His performances and his goals are the reason we have had to redecorate the Champions Wall so often. His achievements here will stand the test of time.
“I know he will be a big success at Monaco. I’m sure we will look on with a mix of celebration and envy as he progresses and flourishes there. He leaves with our appreciation and best wishes. Thank you, Taki.”
