Nielsen began his youth football by the local club Hjørring IF and with them his professional career in 1966, before moving to KB in 1970.
Due to financial reasons Winterthur sold Nielsen to FC Basel during the summer break.
[2] Nielsen joined Basel's first team for their 1974–75 season under head coach Helmut Benthaus.
Nielsen retired from his football career at the end of the 1981–82 season due to an injury caused by a serious foul in December 1981.
The trained banker Eigil Nielsen then moved to live on the island of Fuerteventura for around ten years.
He then returned to his hometown of Hjørring in northern Jutland, where he opened a sporting goods store, which he sold when he fully retired.