Ekman, the son of an oceanographer, was born in the Swedish capital of Stockholm and educated at the University of Uppsala, graduating in 1902. He worked at the International Laboratory for Oceanographic Research in Oslo (1902–08) before he moved to Lund, Sweden, as a lecturer in mathematical physics, being made a professor in 1910.

In 1905 Ekman published a fundamental paper, On the Influence of the Earth's Rotation on Ocean Currents. This work originated from an observation made by the explorer Fridtjof Nansen that in the Arctic drift ice did not follow wind direction but deviated to the right. He showed that the motion, since known as the Ekman spiral, is produced as a complex interaction between the force of the wind on the water surface, the deflecting force due to the Earth's rotation (Coriolis force), and the frictional forces within the water layers.

Ekman also studied the phenomenon of dead water, a thin layer of fresh water from melting ice spreading over the sea, which could halt slow-moving ships. This, he established, resulted from the waves formed between water layers of different densities. The Ekman current meter, invented by him, is still in use.