All three finalists for the award came from the Premier League and Klopp edged out Pep Guardiola and Mauricio Pochettino.
Guardiola led Manchester City to a second successive Premier League title, narrowly beating Klopp and Liverpool.
Pochettino’s Tottenham were Liverpool’s opponents in the Champions League final after a memorable run to the Madrid showpiece.
Klopp attended the ceremony at Milan’s Teatro alla Scala and said: “Mauricio – we won that game. That’s why I’m here, not you.
“That’s how football is, but we all know what an incredible job you did, what an incredible job Pep did, what so many
coaches out there did.
“I have to say thank you to my outstanding club Liverpool FC, to the owners, I have to say they gave me an incredible team, and I have to thank my team, because as a coach you only can be as good as your team is.
“I’m really proud of being the manager of such an incredible bunch of players.”
Klopp took the opportunity to reveal he had signed up to the Common Goal movement, which involves members donating one per cent of their salary to a charity which funds organisations around the world that use football to tackle social issues.
He said: “I’m really proud and happy that I can announce that from today on I am a member of the Common Goal family.”
Having then received a round of applause, Klopp said: “A few people obviously know it – if not, Google it. It’s a great thing.”