With his father, Johann Reinhold Forster, he emigrated to England in 1766. Both were invited to accompany Capt. James Cook (Cook, James) on his second voyage around the world (1772–75). Georg Forster's account of the journey, A Voyage Towards the South Pole and Round the World (1777), was based on his father's journals; it later appeared in a German version, Reise um die Welt (1778–80). A work of travel, science, and literature, the book not only established Forster as one of the most accomplished stylists of the time but also influenced German scientific and literary writing, including that of Johann Wolfgang von Goethe, Johann Gottfried von Herder, and Alexander von Humboldt. A superb essayist, Forster contributed to the scientific, especially botanical, knowledge of the South Seas.

He held professorships at the University of Kassel (1778–84), and at the university at Wilno (now Vilnius, Lithuania; 1784–87), before becoming librarian at the University of Mainz. Sympathetic with the French Revolution, he championed the republican government in Mainz, occupied by the French in 1792, and in 1793 he went to Paris to negotiate on its behalf. Meanwhile the Germans seized Mainz. Forster spent his final days in Paris, reviled among Germans as a traitor and disillusioned by the excesses of the Reign of Terror.