The former Manchester United striker had been Cardiff chairman Mehmet Dalman’s first choice, despite his relatively limited managerial experience with Norwegian club Molde.
Solskjaer replaced the sacked Malky Mackay, who was was dismissed after a series of disputes with club owner Vincent Tan.
But Solskjaer denied he had reservations about working with Tan, or that his former Manchester United boss Sir Alex Ferguson had advised him to turn down the job.
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).”
Solskjaer, who took over a side sitting one point above the Premier League relegation zone, made it clear he had received assurances he would be the main man when it came to football decisions.
“I have had great chats with the owner and Mehmet and they have told me they want me to be in charge of the football and for me I do not need any more confirmation,” he added.
“I go into this with my eyes open and I want the fans to be proud of us when we go on the pitch.”
Cardiff were relegated from the Premier League that season and Solskjaer was sacked after less than nine months in charge with the Bluebirds sitting 17th in the Championship.