Liverpool's 30-year wait for an English league title came to an end this week when closest rivals Manchester City ran out of games with which to catch them.
A dominant season by the men from Anfield has seen them secure Premier League glory with a record seven games to spare.
There might be considerable envy from supporters on the blue side of the city, but Ancelotti has only praise for Liverpool and Klopp.
He told Sky Sport Italia: "I have a great relationship with him. We met last week when everything was virtually decided and I congratulated him.
"Klopp is the architect of this success. Not only for this victory in the Premier League, but for everything he's managed to achieve since arriving five years ago.
"With patience, he's succeeded in building a perfect machine."
Ancelotti lives in Crosby, away from the bustle of Liverpool, but reported hearing "a few bangs" after the Reds' long-awaited triumph was confirmed on Thursday.
Although he has Liverpool midfielder Georginio Wijnaldum as a neighbour, Ancelotti said the Dutchman was out celebrating so not at home.
Everton face a stiff task to close the gap on their local rivals, but the appointment of Ancelotti in December looked a possible watershed moment for them.
He has not yet been able to nudge the Toffees into a European place, but despite sitting 12th in the Premier League they remain in that race, given seventh-placed Tottenham are just four points better off.