Australian Brabham passed away at his home on the Gold Coast on Monday morning.
He won the F1 world title in 1959 and 1960 with the Cooper team and in 1966 in a car he had manufactured himself, the Brabham BT19, as well as taking the constructors' crown in 1967.
Stewart - another three-time F1 title winner, with the first coming in 1969, Brabham's penultimate season before retiring - said: "It is a great loss to motorsport.
"Although he had been ill for some time, I saw him this year in Australia and we had a good chat.
"Jack was a fierce competitor and a modest and almost shy man, but a great three-time world champion who accomplished more than any other driver in the history of Grand Prix racing.
"Not only did he win the world championship three times, but he won driving his own car, which is a feat I suspect will never be matched.
"He was probably one of the most difficult men to overtake."