The US-led 12-nation agreement was set to cover 40% of the world's economic output.
Pulling out of the TPP was one of Mr Trump's first executive orders and fulfils a long-held campaign promise.
Australia has already devised a name for a possible new agreement: TPP 12 Minus One.
The country's trade minister Steve Ciobo said Australia would not abandon the TPP just because it would require "a little bit of elbow grease" to keep it alive.
