Laverty joined United in 1956 and made eight first-team appearances, making his debut in a 5-0 win over Barnsley. He also scored twice against Sheffield Wednesday in a County Cup final.
A statement from United added: “The inside forward left the Lane for Southend in July 1960 and made 21 League appearances for them before going into non- league football.
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“He was later assistant manager to the legendary Geoff Hurst at Telford. Laverty was very proud of his time as a Blade and loved his time in Sheffield.
“Our sincere condolences go out to his family at this sad time.”