Solskjaer had already brought in Magnus Wolff Eikrem from Heerenveen and 18-year-old Norway international Daehli becomes the latest addition.
The Cardiff boss did not reveal how much the teenager had cost, but explained Daehli rejected the chance to return to Manchester United, who had the chance to buy him back after selling him to Molde last summer.
Solskjaer said: "I am pleased to announce we have signed Mats from Molde, we had some competition and I'm glad to say he has chosen to come to Cardiff instead of going back to where he was before.
"He had talks with United, they had the option to bring him back as part of the deal with Molde but he has decided to come here and that shows his desire to do well here."
- Sports & Recreation
- Manchester United
- Magnus Wolff Eikrem