The British-born director died after jumping from a bridge in Los Angeles at the weekend.
"Tony was my dear friend and I will really miss him," a statement issued by Cruise read. "He was a creative visionary whose mark on film is immeasurable.
"My deepest sorrow and thoughts are with his family at this time."
Cruise is claimed by The Hollywood Reporter to have met Scott last Friday, discussing a possible sequel to Top Gun.
Denzel Washington has also paid tribute to Scott.
Speaking to E! Online, he said: "Tony Scott was a great director, a genuine friend and it is unfathomable to think that he is now gone.
"He had a tremendous passion for life and for the art of filmmaking and was able to share this passion with all of us through his cinematic brilliance. My family sends their prayers and deepest condolences to the entire Scott family."
Meanwhile, Scott's family have denied that he was suffering from an inoperable brain tumour.
TMZ reports that his wife has told investigators that her husband did not have any serious medical condition that might have caused him to take his own life.
Watch MTV News on the hour every hour on MTV - Sky Channel 126 and Virgin Channel 134