Titled in honour of the racing legend and national treasure, who passed away at age 88 in May, the trophy’s new name will complete a tribute already evident in its design.
The current trophy features a laminated and studded timber trim and three-spoke design, inspired by the steering wheel in the Cooper Climax racing car that Brabham piloted to his first F1 victory in 1959.
The news comes just hours after Australia's latest F1 star, Daniel Ricciardo, took his first F1 win in Canada.
The late Sir Jack's wife, Lady Brabham, said the renaming of the trophy was a touching gesture.
"I have been overwhelmed by the tributes that have been pouring in from around the globe. It has been comforting to hear kind words from the likes of Jean Todt, Sir Stirling Moss, Sir Jackie Stewart to Alan Jones. Jack would have been so very proud."
The trophy will join a number of other tributes in honouring the great late Sir Jack, with a new plaque unveiled at Albert Park last year and a permanent exhibition of his championship-winning BT19 opened at the Victorian Historic Racing Register in Melbourne.
Sydney Motorsport Park’s Long Track has also been named in honour of the legend, titled Brabham Circuit in 2012.
A special tribute to Sir Jack will also be held this weekend at the Gnoo Blas Racetrack - Sir Jack Brabham Park - in Orange, New South Wales, this week.