Solskjaer, 40, was presented to the media on Thursday having succeeded Malky Mackay as Bluebirds' boss just six days after the Scot was sacked.
Mackay's dismissal, after a series of disputes with owner Vincent Tan, had caused uproar among Cardiff fans but many are pleased by the decision to bring in former Manchester United striker and Molde coach Solskjaer.
Solskjaer takes over at a side who are just one point and one place above the drop zone with testing fixtures against West Ham, Manchester City and Manchester United coming up in the Premier League.
Such is the tight nature of the bottom half of the table, Cardiff are only three points behind Swansea, who they beat 1-0 at Cardiff City Stadium back in November.
Survival remains Cardiff's priority but Solskjaer sees no reason why the Bluebirds cannot finish ahead of their neighbours.
"Short-term it is important we start getting points. We have seven games against sides who are 10th and lower at home so we have a good chance of getting points and results," said the Norwegian.
"But the most important thing is we start getting performances again, then you have the long-term plan.
"I would like us to finish above Swansea. They've almost gone forward as a little bit of a role model, Southampton as well - they're the clubs I've looked at and seen what they've done over the last few years.
"But let's make sure we get above Swansea. I know that will be important for everyone here."
Given the manner in which Tan and Mackay's relationship deteriorated so rapidly, Solskjaer would have been forgiven for seeking assurances over the job he was walking into when he held discussions with the owner and chairman Mehmet Dalman.
Some bookmakers already have Solskjaer, who won two league titles and one Norwegian cup with Molde, odds-on to survive less than 18 months in his new job.
But promises have been made regarding the January transfer budget and the working structure at the club, and Solskjaer does not envisage having any issues when it comes to running football matters.
''I'm very confident in my own ability as a manager and I'm looking forward,'' said Solskjaer, who has signed a rolling contract and brought former United youth coaches Richard Hartis and Mark Dempsey with him to Cardiff.
''I've had great chats with the owner and Mehmet, the important thing now is that we have good dialogue about how to progress the club.
''That's the key for me now, that we do communicate. Mehmet and I will be speaking very often. I'll be in charge of football matters.
''I go into this with my eyes open and I want the fans to be proud of us when we go on the pitch."