Steller was born in Windsheim, near Nuremberg, son to Johann Jakob Stöhler (after 1715, Stöller) and studied at the University of Wittenberg. He then traveled to Russia, arriving in November 1734. He met the naturalist Daniel Gottlieb Messerschmidt (1685 – 1735) at the Imperial Academy of Sciences. Two years after Messerschmidt's death, Steller married his widow and acquired notes from his travels in Siberia not handed over to the academy.

Steller heard about Vitus Bering’s Second Kamchatka Expedition, that had already left St Petersburg in February 1733. He volunteered to join it and was accepted. He then left St Petersburg in January 1738, met Johann Georg Gmelin in Yeniseisk in January 1739 and finally reached Okhotsk and the main expedition and Bering in March 1740.

In September 1740, the expedition sailed to the Kamchatka Peninsula. Steller spent the winter in Bolsherechye, where he helped to organize a local school. He was then appointed to join Bering on the voyage to America. The expedition landed in Alaska at Kayak Island on Monday 20 July 1741, staying only long enough to take on fresh water. During this time Steller became the first European naturalist to describe a number of North American plants and animals, including a jay later named Steller's Jay.

On the return journey the expedition was shipwrecked on what later became known as Bering Island. Here Bering died, and almost half of the crew perished from scurvy. The remaining men settled with little food or water only to survive the winter, the camp plagued by arctic foxes. Despite the hardships of overwintering, Steller studied the flora, fauna and topography of the island in great detail. Notably, he collected the only detailed behavioral and anatomical observations of the Steller sea cow, a large sirenian mammal whose global range was confined to the shallow kelp beds around the Commander Islands and which was driven to extinction within 30 years of discovery by Europeans.

Based on these and other observations, Steller later wrote De Bestiis Marinis, describing the fauna of the island, including the Northern Fur Seal, the Sea Otter, Steller's (or Northern) Sea Lion, Steller's Sea Cow, Steller's Eider and Spectacled Cormorant. Steller claimed the only recorded sighting of the marine cryptid Steller's Sea Ape.

In the spring the crew constructed a new vessel to return to Avacha Bay and nicknamed it The Bering. Steller spent the next two years exploring the Kamchatka peninsula. He was recalled to Saint Petersburg but caught a fever on the journey and died at Tyumen.

His journals did reach the Academy and were published by Peter Simon Pallas and were later used by other explorers of the North Pacific, including Captain Cook.

There is a secondary school in Anchorage, Alaska named after him. Animals and plants named after Georg Steller include: Steller's Eider (Polysticta stelleri), Steller's Jay (Cyanocitta stelleri), Steller's Sea Eagle (Haliaeetus pelagicus), Steller's sea cow (Hydrodamalis gigas), Steller's sea lion (Eumetopias jubatus), Gumboot chiton (Cryptochiton stelleri), Hoary Mugwort (Artemisia stelleriana), Stellera L. (Thymelaeaceae).