England international Henderson, who has been out injured in recent weeks and will miss Sunday's season finale at Newcastle United, was urged by Klopp to "enjoy the moment".
The 30-year-old midfielder joined Liverpool from Sunderland in 2011 and also led the team to Champions League glory last year.
In a video message to Henderson, Klopp said: "Hi my friend. One of the big questions in football is: what makes a proper player? What's more important? Is it talent or is it attitude?
"I think the easy answer is: without talent, you're nothing; without attitude, you will stay a talent forever. You are the perfect example that a mix makes a difference.
"So who would have thought that the young fella coming from Sunderland to Liverpool with big dreams would be one day the best player of the Premier League?
"Maybe you dreamt it. I'm not sure you thought it will happen but I know you are confident enough to have big dreams.
"But now is the moment where everybody saw it. Everybody saw what a great player you are, everybody saw what a great personality you are, what a great character you are.
"I know the human being behind the player and you would have deserved an award for that as well. So, many congratulations, well deserved, outstanding achievement.
"What a year you had, what a career so far you had, and the best news, there's still a lot to come.
"I wish you a wonderful day, enjoy the moment because you can enjoy it, you don't have to play at the weekend at Newcastle.
"Enjoy the moment and, again, best player of the Premier League, wow!"