Bergeron, who was born in Stockholm, studied at the universities of Stockholm and Leipzig. During the period 1925–28 he worked at the famous Geophysical Institute at Bergen before taking a teaching appointment at Oslo University (1929–35). He held various appointments in the Swedish Meteorological Institute and was elected to the chair of meteorology at Uppsala in 1947.

Bergeron is best known for his work on cloud formation and in 1935 published the fundamental paper On the Physics of Clouds and Precipitation. Clouds consist of minute drops of water, but these drops will only fall as rain when they coalesce to form sufficiently large drops. Bergeron considered various processes, such as electric attraction and collisions caused by turbulence, but dismissed these as being too slow and inefficient. He therefore proposed a mechanism in which both ice crystals and water droplets are present in clouds. The water droplets tend to evaporate and the vapor then condenses onto the crystals. These fall, melt, and produce rain. Thus all rain, according to Bergeron, begins as snow and without the presence of ice crystals in the upper reaches of clouds there can be no rain. This theory was supported by the experimental and observational work of Walter Findeisen in 1939 and became known as the Bergeron–Findeisen theory. It does not explain precipitation from tropical clouds where temperatures are above freezing point.

Bergeron also produced important work on weather fronts, methods of weather forecasting, and the growth of ice sheets.