Leo began his career with Burscough and Ellesmere Port Town before signing as a professional with Rochdale. He was leading scorer for Rochdale in the 1973-74 season before arriving at Seel Park initially on loan in January 1975. He scored 15 goals in 18 games before the season’s close and then scored 20 goals in 58 appearances the following season.

In 1976-77 Skeete broke the Club’s post war scoring record netting 45 in 60 appearances. The next year he won the first of two successive Player of the Year awards while scoring 26 goals in 57 games. 1978-79 saw Skeete lead from the front as Mossley won the NPL League and Cup double scoring 26 goals in 53 games and was team captain as Mossley retained the League title in 1979-80 and reached Wembley in the FA Trophy. He scored 29 goals in 55 appearances that season and 19 in 42 in 1980-81.

The 1982-83 season was to be his last at Mossley and he scored 7 goals in 14 games before a £3,500 move to Runcorn. He ended his playing career two seasons later with Altrincham. Leo Skeete made a total of 350 appearances for Mossley scoring 174 goals.