He was called up to represent Denmark at the Euro '96 tournament hosted by England, where he scored one goal in his only match, the 3–0 win against Turkey.
After Euro 1996, Brøndby received a transfer fee of £1.65 million, when Nielsen moved to England to play for Premier League club Tottenham Hotspur.
In the final minute, he scored a diving header to give Tottenham a 1–0 win against Leicester City, and Nielsen was subsequently honoured as "Man of the Match".
[2] Following controversies with Tottenham manager George Graham, Nielsen moved down a league in March 2000, when he was loaned out to Wolverhampton Wanderers in the English First Division in a three-month deal.
He was signed by Watford manager Graham Taylor for £2.5 million, which at the time was the highest fee the club had ever paid for a player.
After three seasons at the club, Nielsen returned to Denmark in 2003 for Superliga relegation battlers Herfølge in a role as player/assistant coach.