He was educated at Melbourne Grammar School, where he first developed his love of polar literature, and at the Royal Geographical Society in London, where he studied surveying and navigation.
Rymill prepared himself for polar exploration with alpine experience in Europe, flying lessons at the de Havilland Aircraft Company Limited, Hendon and courses at the Scott Polar Research Institute, Cambridge, under Professor Frank Debenham. In 1931 he was appointed to the British Arctic Air Route Expedition to Greenland (1930-1931) as surveyor and pilot.
As a result of this, Rymill determined to mount an Antarctic expedition to South Graham Land and the Weddell Sea south of Cape Horn, South America.
After some difficulties securing sponsorship, he purchased an old sail training ship which he renamed Penola and with volunteer staff from Cambridge University and nine crew supplied by the Royal Navy, sailed to the South Atlantic, where their first base was South Georgia. His British Graham Land Expedition (1934-1937) discovered a southern, permanently frozen channel, later named George VI Sound, extending to the Bellingshausen Sea.
In 1938, after completing the official account of the expedition Southern Lights, Rymill married Doctor Eleanor Mary Francis (17 June 1911 – 14 April 2003), a geographer whom he had met at Cambridge. They returned to Australia to live at and manage the Old Penola Estate, and Rymill served as a district councillor.
During World World War II he was commissioned in the Royal Australian Naval Volunteer Reserve.