The legendary broadcaster died at his New York home with his family at his bedside after a long illness, aged 92.
Cronkite fronted the evening news for TV network CBS from 1962 to 1981.
Former action star-turned-California Governor Schwarzenegger was saddened to hear of his passing, and described him as "the most trusted man in America."
He says, "For decades, Walter Cronkite was the fixture in American living rooms whose reassuring voice reported on some of the most important moments in our nation's history. He was the most trusted man in America who calmly explained monumental events such as the Vietnam War, Watergate, and the moon landing -- events that shaped and defined a generation.
"Walter remains the benchmark for what it means to be a television journalist and he will be missed. Maria and I join all Californians in expressing our sadness over his passing and we send our thoughts and prayers to Walter's family and friends."
Ocean's Eleven star Clooney was also full of praise for Cronkite: "He was the most important voice in our lives for 30 years. And that voice made people reach for the stars. I hate the world without Walter Cronkite."
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