Ali died on June 3 at the age of 74, following a 32-year battle with Parkinson's disease. His passing emerged days after he was admitted to a medical center in Phoenix, Arizona, for respiratory complications.
Smith, who earned his first ever Oscar nomination for his role as the outspoken sports star in Ali, took to Facebook to honour the man he had come to call a friend.
"You shook up the World! My Mentor & My Friend. You changed my Life. Rest in Peace," the 47-year-old actor wrote.