Scottish-born McCallum died of natural causes on Monday, surrounded by family at New York Presbyterian Hospital.
US broadcaster CBS said in a statement: 'David was a gifted actor and author, and beloved by many around the world.
'He led an incredible life, and his legacy will forever live on through his family and the countless hours on film and television that will never go away.
McCallum had appeared in such films A Night to Remember (about the Titanic), The Great Escape and The Greatest Story Ever Told (as Judas).
But it was spy drama, The Man From U.N.C.L.E. that made McCallum a household name in the mid-'60s.