Moller Nielsen had been ill since undergoing an operation for a brain tumour in July last year.
After ending his seven-year playing career with Odense, his hometown club, in 1962, he went on to coach several Danish clubs, as well as the Finland and Israel national teams, in a coaching career that spanned four decades.
The highlight was Euro 92 in Sweden, when Denmark were a late replacement in the tournament for the former Yugoslavia, and under Moller Nielsen went on to clinch the title with a 2-0 victory over Germany in the final.
(Reporting by Teis Jensen, editing by Stephen Wood)
