Brabham, who won the title in 1959, 1960 and 1966 and is the only man to have won the championship driving a car bearing his name, died at his home on Australia's Gold Coast on Monday at the age of 88.
Webber, who over the last decade came closer than any other driver to giving Australia a third world champion after Brabham and Alan Jones, said he had been "saddened" to hear news.
"He is the epitome of a champion racing driver and a true blue Aussie," he said in a statement.
"He was a trailblazer; he took the hardest road and made it easier for the rest of us to follow.
"When I think of Jack, I think of a tenacious individual; an absolute grafter; he did it his own way and made it stick. There were no real rules or a manual for Jack; he figured it for himself.
"What he achieved taking on the best in the world and winning one of his three world titles in his own machinery is the stuff of pure legends."
Webber, who retired at the end of last season after 215 grands prix starts over 11 years in Formula One, said he had been "blown away" when he met Brabham in his late teens and "Black Jack" had become a close confidante during his career.
"After hearing the rumours that I might move to Ferrari, he told me he would be very disappointed if I went there because for him, it was the absolute betrayal because they were his motivation – the ones he wanted to beat in his day!" the 37-year-old added.
Webber, who emulated Brabham by winning both the Monaco (twice) and British races, said the "inspirational Aussie battler" would never be forgotten.
"Although I was unable to repay that support by joining him and Alan Jones as world champions, I gave him some very happy moments by winning some of the more prestigious special grands prix," he said.
(Reporting by Nick Mulvenney, editing by Ian Ransom)
