The Reds ended a 30-year wait for top-flight glory in a season that also saw them crowned world champions following on from last year’s Champions League success.
The award was announced by ex-Manchester United boss Sir Alex Ferguson, after whom the trophy is now named.
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“Jurgen, fantastic,” Ferguson said on Sky Sports. “We speak about Leeds spending 16 years in the Championship, but Liverpool 30 years since winning that league, incredible.
“You thoroughly deserved it. The performance level of your team was outstanding. Your personality runs right throughout the whole club. It was a marvellous performance.
“I’ll forgive you for waking me up at 3.30am to tell me you have won the league! Thank you, but anyway, you thoroughly deserved it. Well done.”
Klopp declared himself “absolutely delighted” to get the award, which he dedicated to his staff.
And the 53-year-old said he was honoured to be handed a trophy named in honour of Ferguson.
“I know it’s not 100 per cent appropriate as a Liverpool manager but I admire him,” he said. “I remember he was the first British manager I met.
“We had breakfast. I’m not sure how much he remembers but I remember because for me this moment was like meeting the Pope. It was absolutely great and from that first season we clicked.
“I didn’t think at this moment I would have a trophy in my hands named after him.”
Last year’s winner Chris Wilder had to settle for the runner-up spot this time around after narrowly missing out on Europe in a remarkable return to the Premier League for Sheffield United.
Also short-listed were Wycombe boss Gareth Ainsworth and Leeds’ Marcelo Bielsa, who was named Championship manager of the year after earning the title.
Coventry boss Mark Robins took the League One award and Crewe’s David Artell was named League Two manager of the year.
Emma Hayes was named Barclays FA Women’s Super League manager of the year after leading Chelsea to a league and Continental Tyres League Cup double, while Aston Villa’s Gemma Davies took the FA Women’s Championship award after a curtailed campaign.
The Premier League manager of the year will be awarded separately next month.