Mignolet has joined Club Brugge in his native Belgium in a deal worth an initial £6.4m, with the hope of securing first-team football.
The 31-year-old acted as an understudy to first-choice Liverpool goalkeeper Alisson last year, having been denied a loan move to Napoli.
Liverpool were once again reluctant to let Mignolet go, believing him to a model professional and ideal goalkeeping cover.
But with former West Ham ‘keeper Adrian signed on a free transfer, Mignolet has been granted permission to leave Anfield.
“If you were to ask me to write a list of the most standout professionals I’ve worked with in the game – in a career of well over 30 years – Simon Mignolet would be competing for the number one spot,” Klopp told the club’s official website.
“The respect he commands in our dressing room is unrivalled. An outstanding athlete, an outstanding person, and an international-class ‘keeper.
“The truth is I don’t want Simon to leave – why would I? He’s a ‘keeper good enough to start for all the teams in the Premier League.
“But this is a little like the situation we faced with Lucas Leiva a few seasons ago now. Sometimes you have someone whose contribution to the club means you have to consider their welfare also. Simon is such a person.”
Mignolet joined Liverpool under Klopp’s predecessor Brendan Rodgers in 2013, establishing himself as their first-choice goalkeeper for the following three seasons.
However, upon Klopp’s arrival, competition for the No 1 spot increased and Mignolet spent another two campaigns rotating with new signing Loris Karius.
Last year, following Karius’ two-year loan move to Besiktas, Mignolet was retained as a reserve goalkeeper and made only two appearances, both in the domestic cups.
The Belgium international leaves having made 204 appearances for Liverpool in total since arriving from Sunderland six years ago.
“The service he has given this club during his time here means I cannot ignore an opportunity for him that will impact so positively on his future,” Klopp added.
“I think what he has done for LFC means he earns the right to do something that helps him in this moment.
“Brugge are so lucky to have him. The shape he is in – the quality he has – he could play 10 years for this team if both want that.
“I will always be grateful for everything Simon has done for me and the staff while we have been here and I know his teammates will miss him also.
“But we say farewell and good luck with a host of happy memories and we tell him the best seats in the house are available to him and his family whenever they want to come back to Anfield in the future.”