"Robert and I worked together for many years and losing him is like losing a part of me. My deepest sympathies go out to Linda and the Vaughn family," he said.
Vaughn, who was "a few months shy of 84" had been seeking treatment for his leukaemia, Mr Sullivan said.
"He was a great human being. I enjoyed every day of working with him," he said.
Vaughn had only recently finished two projects - an appearance on Law and Order: SVU, and a starring role in the upcoming film Gold Star, about a young woman caring for her dying father.
Famous films Vaughn worked on included Bullitt and Towering Inferno, both with Steve McQueen, and he took the role of the villain in Superman III.
He was also well-known in Britain for his 1970s appearance as Harry Rule in the ITV series, The Protectors.
The plot featured three wealthy individuals getting together each week, usually in exotic locations, to solve crimes and protect the innocent.
Though extremely popular, it was later described by Vaughn in his autobiography as "tasteless junk".
Decades later, he would have another hit UK series with Hustle, a BBC series in which he played elderly con man Albert Stroller, responsible for setting up potential targets for a younger generation of grifters.
He is survived by his wife Linda and two children, Cassidy and Caitlin Vaughn.
On social media, fans paid tribute to his work.
"Robert Vaughn, such a fine actor, one of the best Columbo villains (no higher praise than that) and an utterly charming man," tweeted Stephen Fry.
Actor Jon Donahue said: "As an 80s kid, I grew up with Superman III... Robert Vaughn was a badass!" referencing Vaughn's role as Superman's nemesis.
Gavin Free, creator of the YouTube series The Slow Mo Guys paid tribute to Vaughn's work ethic. "I got to work with him on Hustle five years ago. He did his own slow mo stunts that day while in his late 70s," he wrote.
Fellow fictional secret agent, Sir Roger Moore, whose incarnation of James Bond came several years after The Man From UNCLE, said he was sorry to hear the news.