The Dutchman had four games in caretaker charge at Old Trafford -- two of them against Leicester -- following Erik ten Hag's sacking at the end of October, but left the club when Ruben Amorim arrived last month.
Van Nistelrooy, speaking at his first press conference since replacing the sacked Steve Cooper at the King Power, said offers had poured in.
"What happened after the games and the amount of interest, the options that all of a sudden were there for me and the options that came along, I was a little bit astonished," he said on Monday.
"It was four games and I managed a full season at PSV (Eindhoven), was able to win the cup and the charity shield. I have been in coaching, in the (under) 19s and the national team (with the Netherlands) and it never got this reaction from the football world.
"It provoked these reactions and I was only happy with that -- and to get in conversations with different parties and be able to make a decision which felt really good for me and I am happy to be here."
He said he had enjoyed his "intense" spell in the Old Trafford hot seat and had helped "steady the ship".
"I really enjoyed it, being responsible, creating a connection with the team, with the supporters and turning the momentum for the club for a little bit," he added.
"That is our job and that felt great to do and it just got better now I am in this position to do it again."
Van Nistelrooy, whose first game in charge of Leicester is against West Ham on Tuesday, takes over a side just a point above the relegation zone after 13 games.
Caretaker boss Ben Dawson oversaw Saturday's 4-1 loss at Brentford, the team's third straight defeat.
Van Nistelrooy, a former striker for United and Real Madrid, said he was proud to have been given the opportunity to manage the former Premier League champions, where "expectations are clear".
"It is something we face, that challenge to maintain and play in the Premier League and that is the big target for everybody to achieve that," he said.
The 48-year-old added: "In two days it's difficult to make a lot of changes, but we have started to make changes in the style of play, training sessions, structure, little by little starting to build a foundation of a highly motivated team who can compete in this league."
© 2024 AFP