Rossby was born the son of an engineer in Stockholm and educated at the university there. In 1919 he joined the Geophysical Institute at Bergen, which at the time, under Vilhelm Bjerknes, was the world's main center for meteorological research. In 1926 he emigrated to America and was appointed professor of the first meteorology department in America at the Massachusetts Institute of Technology in 1928. After two years as assistant head of the Weather Bureau he became professor of meteorology at the University of Chicago in 1941.

Rossby carried out fundamental work on the upper atmosphere, showing how it affects the long-term weather conditions of the lower air masses. Measurements recorded with instrumented balloons had demonstrated that in high latitudes in the upper atmosphere there is a circumpolar westerly wind, which overlays the system of cyclones and anticyclones lower down. In 1940 Rossby demonstrated that long sinusoidal waves of large amplitude, now known as Rossby waves, would be generated by perturbations caused in the westerlies by variations in velocity with latitude. Rossby also showed the importance of the strength of the circumpolar westerlies in determining global weather. When these are weak, cold polar air will sweep south, but when they are strong, the normal sequence of cyclones and anticyclones will develop.

Rossby is credited with having discovered the jet stream. He also devised mathematical models to predict the weather which were simpler than those of Lewis F. Richardson. His school provided the ‘dynamic meteorology’ that allowed, with the coming of computers and weather satellites, the long-term prediction of weather.