Norwegian Solskjaer, who spent 11 years at United as a striker between 1996 and 2007 and scored 126 goals, was given the caretaker role until the end of the season on Wednesday following the sacking of Jose Mourinho.
He also promised fans that he would "give everything" to "bring the club success" and get players "enjoying football".
He will do so having promised the players a chance to prove themselves all over again after some fell out of favour under Mourinho.
"I dreamed when I was a kid that I would play for one of the world's biggest teams and it did happen".
Solskjaer's spell as United boss will start with a trip to Cardiff, where he was sacked after just nine months in 2014.
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'I was happy [with the draw], they will be two great matches between two great sides, ' said the Brazilian.
Solskjaer's presence rekindles memories of United's golden age, but also serves as a stark reminder of how far the club have fallen since the retirement of Alex Ferguson in 2013.
Sources have told ESPN FC that Pochettino remains United's top target, even though the Argentine is under contract at Spurs until 2023.
Speaking to Manchester United's own TV station in early August, Mourinho said: "If we don't make our team better it will be a hard season" adding "My CEO [executive vice-chairman Ed Woodward] knows what I want". If he wants the job, then he's definitely the man. I'll need that break, too, at some point.
During his first appearance before the media as United manager, he said: "I will have an input, of course". But you look at the merits, you pick a team now and you move on. They've got nowhere to hide now, especially Paul Pogba.
"When you're at Manchester United there are a set of demands and one is to be a team player and I don't think anyone has been on the bench more than me!"