The former Manchester United youngster is reunited with his former manager, becoming the second Norwegian player to join the Bluebirds after Magnus Wolff EikremCardiff City have completed the signing of Mats Moller Daehli from Molde.
The 18-year-old is reunited with new Bluebirds manager Ole Gunnar Solskjaer, who recruited him for the Norwegian club in July 2013 after spending nearly three years in Manchester United's youth system.
Solskjaer described Daehli, who made an early impact at Molde despite his age, as "on a par with Adnan Januzaj" in September.
The youngster becomes Cardiff's second signing of the January window, following countryman Magnus Wolff Eikrem, who made his debut off the bench in Saturday's 2-0 defeat at home by West Ham.
Daehli is one of Norwegian football's top talents and has already made two appearances for the national team.