Moller Nielsen struggled to return to health after undergoing surgery for a brain tumour last July and passed away on Thursday morning.
After his playing career was cut short due to injury, he began to forge his reputation as a coach within Denmark, becoming national team coach in 1990 and guiding them to their only major trophy two years later.
Denmark earned a late entry to Euro 92 after Yugoslavia were forced to withdraw, and they took full advantage, beating Germany 2-0 in the final.
Goalkeeper Peter Schmeichel produced an excellent display in that match and was named in the team of the tournament, and the former Manchester United man led the tributes to his former coach.
During his six years in charge of Denmark national team Moller Nielsen presided over 73 games, collecting 40 wins, 18 draws and 15 defeats.
Richard Møller Nielsen, an inspiration, my teacher and my friend. R.I.P my friend. pic.twitter.com/g30xmVNnTt— Peter Schmeichel (@Pschmeichel1) February 13, 2014
After leaving his role with Denmark in 1996 he went on to coach Finland and Israel at international level before retiring in 2003.