"Sydney made the world a little better, movies a little better and even dinner a little better," the actor – who worked with Pollack in 2007's Michael Clayton – said in a statement.
Pollack, most famous for directing Out of Africa, Tootsie and They Way We Were, co-produced and starred in Clayton. (He also served as executive producer for Clooney's Leatherheads.)
"A tip of the hat to a class act," Clooney's tribute continued. "He'll be missed terribly."
At the time of his death, the Oscar-winning director was surrounded by family at his home in Pacific Palisades, said his publicist Leslee Dart.