The 40-year-old had been Cardiff chairman Mehmet Dalman's first choice from the outset, and the Norwegian's appointment appeared inevitable after he attended the Bluebirds' defeat at Arsenal with Dalman and owner Vincent Tan.
There has been surprise in some quarters that Solskjaer has taken on the task of working with Tan, particularly after reports earlier in the week that he had reservations in the wake of the Malaysian's disputes with Mackay over recent months, and that Ferguson had told him to turn down the job.
But Dalman's promise of money to spend in January and reassurances over the working structure at the club have convinced Solskjaer, who has signed a rolling contract, to come on board.
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)."
But Solskjaer, who met the Cardiff squad on Thursday morning, made it clear he has received assurances that he will be the main man when it comes 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.
"I will only ask my players for 100 percent, which was hammered down to me with the gaffer 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."
Solskjaer will bring in former United coaches Mark Dempsey and Richard Hartis to work with him in south Wales as he starts his reign with the Bluebirds one point and one position above the relegation zone after one win from 10 games.
And he revealed he has already had phonecalls from people wanting to work with him at Cardiff.
"What is important is we get continuity and stability," he said. "I have had numerous phonecalls already from agents and staff who want to come and join the club.
"They know it is a great place to work and a great club to work for, so I have to step back and take my time."