Leo VanderElst's older brother was 14 years old when he left local team Mazenzele for Sporting Anderlecht. On a youth tournament in Grimbergen, Polyte Vanden Bossche noticed the player and he advised the club to buy him. Michel Van Vaerenbergh was the trainer who followed Vander Elst.

He made his debute as a 17 years old in a friendly game against Sparta Rotterdam.

Georg Kessler selected him for the first team and he made his debute in the first division against Diest. François Vander Elst was fast and had a good acceleration. He was also very dangerous in the box. But he wasn't always inspired, Kessler put him in different positions on the midfield. In seven years time, he scored almost 80 goals for Anderlecht. Especially in the big European games, he showed what he was capable of. In Sofia, in the season of '77-'78, he scored three goals in eleven minutes. During the final of the Cup Winners' Cup against West Ham (4-2) in 1976, he and Robbie Rensenbrink both scored twice. One year later, he became the best striker in the league with 21 goals ('76-'77). He was selected for the national team for 44 times between '73 and '83.

In 1980, he left Sporting for New York Cosmos. He liked playing for New York, but eventually went to West Ham. He finally came back to Belgium and ended his career at Lokeren.

Aftrer his career, he opened a snooker bar in Opwijk. On New Years day 2017, Vander Elst suffered a serious heart attack and ended up in coma. On January 11, he died.