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 five 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.
Israel FA chairman Avi Luzon said Nielsen had made significant contributions to soccer in the country and was a great ambassador of the game having managed them from 2000-02.
"He was a true friend of Israel, he loved the country and its people and worked for the advancement of Israeli soccer even after he finished his tenure as national team coach," Luzon said in a statement.
"Nielsen was an excellent coach for Israeli soccer and during his time here he instilled advanced and worthy coaching practices.
"Even after he ended his tenure in Israel he was a great ambassador for Israeli football and the state. May his memory be blessed."