He was the son of Major Ole A. Fægri (1875–1962) and Gudrun Stoltz (1881–1940) and the nephew of the botanist, natural scientist, and politician Jørgen Brunchorst (1862–1917).

Fægri received his examen artium at the Bergen Cathedral School in 1926 and received his doctorate in 1934 with the thesis Über die Längenvariationen einiger Gletscher des Jostedalsbre und die dadurch bedingten Pflanzensukzessionen.

He was outspoken in his criticism of the negative effects of hydroelectric power development on nature and biodiversity.

For example, in the 1960s he agitated for a liberal act on use of marijuana, which he saw as something the state should leave to the individual citizen to decide about.

Privately, he was a proponent of naturism and he appeared naked in a discussion on that topic broadcast on Swedish television.