GPS is one of the oldest clubs in Queensland rugby, tracing its heritage back to the Past Grammar club formed in 1887.
According to noted rugby historian Ian Diehm in his book Red! Red! Red!, Past Grammar reformed along with other clubs after the devastation of the first world war, and eventually became GPS in 1931 after a change of constitution, which broadened its membership beyond old boys of Brisbane Grammar.

The first president of the modern GPS was Dr Kenneth Fraser and its first coach Dr "Jacky" Beath, the former Wallaby and Australian Infantry Forces fullback.

Four members of the club - "Blow" Ide, Bill McLean, Boyd Oxlade and Llewellyn "Welly" Lewis went to England with the 1939 Wallabies, but only McLean continued after World War II. McLean was the first of GPS's two Australian captains, Arch Winning being the second.

The club has had many homes: New Farm Park, Finsbury Park and, since 1977, Ashgrove Sports Ground.

Past Grammar had won premierships in 1892, 1898, 1899 and 1914, but had to wait until 1961 to win again as GPS, coached by the former GPS player and later Queensland and Australian coach, the late Bob Templeton.

The club won the premiership again in 1972 and for a third time in 1996, when the A Grade team upset Souths 12-6.

"The GPS club exists to promote and foster excellence and enjoyment in the 'running game' of Rugby Football...
and, in so doing, assist the progress of members along the broader pathway of life.

In pursuit of the mission, we will actively promote the following values: developing the whole person; respecting the individual; respecting individual and group responsibilities; upholding the standards of a responsible community organisation; catering for the needs of players at all levels; and encouraging individual participation."

- GPS Mission Statement