No financial details were disclosed on the deal for Berge, who becomes Burnley manager Vincent Kompany’s eighth new signing ahead of their return to the top flight.
"It’s a great environment full of young talented players from all around the world, so I just think it’s the perfect fit for me," Berge said in a statement.
"The club has high ambitions, making several signings, and it all just fits into what I’m looking for."
Berge joined United in 2020 from Belgian side Racing Genk, with the Yorkshire club reluctantly accepting Burnley's bid.
"Unfortunately, along with his representatives, he has opted to move to Burnley and we would like to place on record our thanks for his service over the past three and a half years," United said in a statement.
