Ruud laments Beckham loss
The England captain completed his big-money move to Madrid on Tuesday and van Nistelrooy believes the midfielder will prove to be a massive loss at Old Trafford.
The Dutch international has backed his former team-mate to be a success in Spain and understands why he decided to leave United.
"When I was at PSV, my dream was to make it to a big club. Now I'm at Manchester United. That is the very top and I can't think of anything better," van Nistelrooy told The Sun.
"Yet I can understand Beckham joining Real Madrid. They are the champions of Spain with a squad full of stars.
"And that is their philosophy. If they could, they would play 11 Beckhams every week."
"David will be a big loss. We will miss him very much. I can only speak for myself, but I will miss him as a man, as a guy in the dressing-room and as a player on the pitch.
"It is great to play alongside him. But certain opportunities come along and the decision was made.
"I can only wish him the very best for his new career in Spain with Real and the new challenge.
"It was still just speculation when I went to the USA. Yet even there it was front page news, so I followed it all the way.
"Even though it became more and more likely he'd go, I was hoping the transfer would not go through. But it has and we must move on.
Van Nistelrooy is also excited at the possible arrival of Brazilian World Cup winner Ronaldinho at Old Trafford despite Paris Saint Germain refusing United's first offer for him.
The Dutchman also revealed he would like to line-up alongside Luis Figo at Old Trafford as United seek a replacement for Beckham.
"Brazilian World Cup hero Ronaldinho is a personal favourite," added van Nistelrooy.
"The prospect of signing Ronaldinho really excites me. He is the type of player who can fit in very well and is the perfect link between the midfield and strikers. I would also be very happy if Figo joined us."