The Cardiff-born winger won 29 Welsh caps during a career that started at Pembroke Borough and ended at Barry Town.
In between, Reece was a hero at Bramall Lane where he netted 59 goals during his seven years with the Blades and played a huge role in United winning promotion back to the old First Division in 1971 - at the expense of his hometown club.
But he suffered with poor health in later years and in April 2000 his right leg had to be amputated after cysts kept appearing behind the knee.
Smith, whose first spell as Wales manager came in the early 1970s, said he was "devastated" to hear of Reece's death.
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