The 20-year-old completed his medical with the club and has signed a four-year-deal at Elland Road which is set to keep him at the club until the summer of 2025.
Klaesson made his Vålerenga debut against FK Haugesund in June 2019 before going on to make a further 56 appearances for the club.
This season, he has made 14 appearances for Vålerenga, who currently sit in seventh spot, halfway through their league campaign.
Klaesson has represented Norway at various youth levels and has amassed 38 caps in the junior ranks for his nation
The youngster will provide competition to the Whites first-choice goalkeeper Illan Meslier, after Kiko Casilla departed the club earlier this summer.
It has been a busy summer for Leeds so far, with Klaesson their sixth arrival of this transfer window, joining Lewis Bate, Junior Firpo, Jack Harrison, Sean McGurk and Amari Miller at the club.
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