Ole Gunnar Solskjaer revealed earlier on Friday that Berget had held talks with the Premier League club, with the move now official after the 23-year-old penning a two-and-half-year deal.
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"I’m delighted to welcome Jo to the club," Solskjaer told the club's official website. "He went through his medical last night and signed his contract this morning.
"He’s a forward and full Norwegian International and arrives on a very good deal for us. He knows the way I want to play, he’s a secondary frontman and is a very strong and intelligent footballer. He’ll do well for us."
Berget started his career at Lyn and had a spell in Italy with Udinese before returning to his homeland.
He made 63 appearances for Molde, scoring 17 goals.
Berget has been capped by Norway four times and now looks set to join Cardiff’s battle to stay in the top flight.