The former Manchester United striker and Molde manager was confirmed as Malky Mackay's successor on Thursday, just six days after the Scot was sacked after a series of disputes with Malaysian Tan.
Given the manner in which Tan and Mackay's relationship deteriorated so rapidly, the 40-year-old 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 the Norwegian, 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.
''I will only ask my players for 100 per cent which was hammered down to me with the gaffer (Sir Alex Ferguson) and Roy Keane at Manchester United. We can forgive mistakes as long as we have a go and enjoy playing in the Premier League.
''I felt I needed to be back here and I want to stay for the long, long term.''
When asked what he had thought of the reports about Tan and Mackay's relationship, he added: "You know, everything isn't exactly what it seems from the outside.
"There has been reports of this, that and the other in Norway as well.
"After talking to Mehmet and saying to my eldest son Noah, 'This looks like what Daddy wants to go for', he wakes up, checks the internet and says: 'Dad, it says you've said no to Cardiff.' So don't always believe what is in the press, no disrespect."
Solskjaer was also quick to dismiss reports that his former manager Sir Alex Ferguson had advised him against taking charge at Cardiff.
He said: "I have had good contact with the gaffer (Ferguson). He has wished me all the best and given me some good advice as he always does.
''When you worked for him you could ask him for advice and I had a good conversation with him.
''It is absolute nonsense (that he told me to turn down Cardiff).''
The first sign of trouble between Tan and Mackay came in October when the Scot's head of recruitment Iain Moody was dismissed over an alleged transfer window overspend of £15million.
Mackay and Moody denied that was the case, but Dalman has revealed the club have altered their approach to transfers in order to allow a greater transparency and prevent any future issues.
He said: "We changed the structure. Until I arrived the board had never met. That was number one.
"The manager will say what he wants: A, B and C. I will go to the board and say, 'Do we have that money?' It gets authorised. It gets signed off. The manager goes and does his thing. Everybody is on the same page.
"Before that did not exist. We have got transparency between the football side and the business side."