The 23-year-old, who announced earlier this week that he was planning to leave Molde, has now finalised his move to the Bluebirds for an undisclosed fee.
"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."
Cardiff are currently at the bottom of the Premier League table.