The Englishman will be Europe's first repeat captain since Bernard Gallacher in 1991, 1993 and 1995.
The move will be welcomed by players who chanted 'two more years' at the trophy presentation in Rome.
"The Ryder Cup means so much to me, so to be captain again and have the chance to create more history by becoming only the second European captain to win back-to-back is exciting," said Donald in a statement on Wednesday.
"There is no question that being a captain away from home is a tough task. But I have never shied away from challenges throughout my career and it is precisely the kind of thing that motivates me.
"I can't wait to get another 12-strong team to Bethpage in 2025."
Europe won 16-1/2-11-1/2 at Rome's Marco Simone course in October.
Donald, who replaced Henrik Stenson after the Swede moved to LIV Golf, has triumphed in all four Ryder Cup appearances as a player and one as captain.
He played in the last European Team to win on American soil at Medinah Country Club in 2012.
"Luke was a superb Captain in Rome and we are delighted that he will be returning to the role for the 2025 Ryder Cup in New York," said Ryder Cup Executive Director Guy Kinnings.
The only Europe captain to lead his team to victory home and away was Tony Jacklin who achieved the double at Muirfield Village in Ohio in 1987 after winning two years previously at The Belfry in 1985.
