Nielsen was awarded the title of International Master by FIDE in 1991 and that of Grandmaster in 1994. He won the Danish Chess Championship five times: in 1996, 1999, 2001, 2003, and 2008. He played for Denmark in seven Chess Olympiads, three times on top board, with an overall result of 60.1% (+24−10=35). He won an individual bronze medal on third board at Moscow 1994.^[1]

On January 30, 2004 he played against ChessBrain – which earned the world record as the largest distributed chess computer. The result was a draw.^[2]

By September 2005, Nielsen's Elo rating in the FIDE list was 2668, at the time the highest rating for any player from the Nordic countries.

Nielsen coached World Champion Viswanathan Anand from 2002 until 2012. Anand won the World Championship title in Mexico 2007, and defended it in Bonn 2008, Sofia 2010 and Moscow 2012.

Nielsen has been coaching world number one, Magnus Carlsen, since 2013.^[3] Carlsen won the Candidates Tournament 2013, which gave him the right to challenge Anand for the world championship. He defeated Anand, and has since defended the title four times.

Nielsen had previously coached Carlsen in Khanty-Mansiysk 2005, where Carlsen became the youngest player ever to qualify for the Candidates' matches.

In 2012 Nielsen began playing shogi; he achieved the mark of 2 dan in May 2017. The same month, he won the Danish Shogi Championship.^[4]

Nielsen lives in Lithuania with his wife, Viktorija Čmilytė-Nielsen, and four children. She is also a chess grandmaster, as well as a politician of the Liberal Movement.^[5]