The German coach took to Instagram to celebrate his old club's success after his successor Arne Slot won the title in his debut campaign as the Reds beat Tottenham 5-1 at the weekend to secure the crown.
Sharing a photo of the celebrations from Anfield, Klopp captioned the post: "Super grateful for the past, super, super happy about the present, extremely positive about the future!
"Congratulations - YNWA [You'll Never Walk Alone]. Thank you - Luv."
Slot sang Klopp's name on the pitch during the celebrations and thanked his predecessor for leaving the club in such a healthy state when he departed last year.
The Dutch coach said: "It feels great. I don't think I want to say a lot. The only thing now is to send my appreciation to Jurgen Klopp."
He added: "I am 99.9 per cent sure that if I pick up my phone there will be a message from Jurgen.
"So many moments in the season the two of us have had contact. I think he showed last season what a wonderful human being he is by introducing me.
"But what mattered most is the team he left behind that was able to win the trophy."
Liverpool had not been expected to challenge for the title in Slot's first campaign and the manager himself understood why some observers thought that.
Slot said: "We started really well and maybe it helped that [Manchester] City had a difficult spell that they have not had in five years.
"When the season started, we would have been happy with top four. But I don't think that is fair on the players as they are much better than that and they have shown it this season."