[1] Brænne was born in Kristiania (now Oslo), Norway.

Randi Brænne was married to two acting colleagues; Frithjof Fearnley (1896–1971) and Frank Robert (1918–2007).

[2][3] She made her stage debut at Det Nye Teater in 1934.

She performed at various theatres including Den Nationale Scene, Trøndelag Teater, Centralteatret, Riksteatret and Seniorteatret.

Among her best-known film appearances were in Du har lovet mig en kone!