"You shook up the World!" he wrote. "My Mentor & My Friend. You changed my Life. Rest in Peace."
Last year, Smith honored Ali at Sports Illustrated's Sportsperson of the Year ceremony, where the Legacy Award was renamed the Sports Illustrated Muhammad Ali Legacy Award. On stage, the Suicide Squad star recalled what it was like to play the three-time World Heavyweight Champion in the 2001 film.
"There's no doubt that he was a great boxer. He was the greatest of all time," Smith said. "When we think about the legacy of Muhammad Ali, what he did in the ring is not what we think about."
"For nearly two years, I worked to transform myself into the man who changed his name from Cassius Clay to Muhammad Ali and shook up the world, and that’s really what makes my job so beautiful," he continued. "As an actor, for four or five months at a time, I get to wear people's lives, so I got to wear Muhammad Ali's greatness. I got to study and feel and embody the soul of the man from the foundations of Islam and the strength of his Muslim faith in his life to the beautiful wake that he always leaves in his magnificent path."
Ali followed a decade of the champion athlete's life starting in 1964, which included his heavyweight title fight against Sonny Liston and being banished from the sport following criticism of the Vietnam War. Smith's portrayal of Ali earned him his first Oscar nomination in 2002. As for Sports Illustrated, the magazine has also named Ali, whose nickname was "The Greatest," the Sportsman of the Century.
Ali died at the age of 74 on Friday following a 32-year battle with Parkinson's disease.
"The Ali family would like to thank everyone for their thoughts, prayers, and support and asks for privacy at this time," family spokesperson Bob Gunnell shared following news of the boxer's death.
A funeral will be held at the KFC YUM! Center in Ali's hometown of Louisville, Kentucky, on June 10. There will also be a procession held throughout the city that same morning in order for mourners to pay their final respects, according to a statement from the family.
It's been a difficult few months for Smith, who also paid tribute to Prince after learning the late singer had died on April 21. "I am stunned and heartbroken," he wrote on Facebook. "I just spoke with him last night."