After joining the Millers in 1945/46, Shaw is best remembered for a club record 46 goals in League and Cup in the 1950/51 season as the Millers won the Third division North Championship.
Jack netted no less than five hat-tricks in that season and also five goals in one game in a 7-2 FA Cup tie win at Darlington.
In total Shaw scored 139 goals in 279 appearances for the Millers before signing for Sheffield Wednesday in what was then the top division of English football.
Treeton born Peter Perry also died earlier this week, with a club spokeman saying: "Jack Shaw was a club legend and a true great from a successful and memorable time in the club's history.
"We were sad to learn of his death, and also that of another stalwart Peter Perry and our thoughts are with their families."
All at MillersMAD pass on their condolences to both families and close friends.