Gallacher made his rugby union debut for Llanelli, for whom he played almost 200 times, in 1965, and won a solitary Wales cap in 1970.
He then switched codes and represented his country in the 1975 Rugby League World Cup.
After retiring, Gallacher stayed in the sport, becoming chief executive at Llanelli and the Scarlets before taking the reigns as chairman of Regional Rugby Wales, a role from which he stepped down in July due to ill health.
"Stuart dedicated his life outside his family to the game of rugby and his contribution down the years will prove a fitting epitaph to his commitment and loyalty," WRU chief executive Roger Lewis is quoted as saying by BBC Sport.
"His understanding and love for the game meant he was always able to contribute positively to important decisions which formed the road map for the development of the sport."
Scarlets players are wearing black armbands in today's European Champions Cup game at Toulon as a sign of respect.