Alnwick Rugby Football Club said it was “deeply saddened” by his death.
“The senior players couldn’t have enjoyed his sessions more and in recent years he has taken to coaching the minis, and I know he will be a huge miss to them.
“Our thoughts are with his wife Anna, son Oscar, mother Christine, sister Emily and the rest of his family.
“A great rugby player and an even better man.”
Mr Voyce, from Truro in Cornwall, played for Wasps, Bath and Gloucester before retiring from the sport in 2013.
Among those who have paid tribute are England head coach Steve Borthwick.
He described Mr Voyce as “a wonderfully gifted rugby player and a truly lovely man”.
“Tom left a lasting impact on everyone who had the pleasure of knowing him and created memories that will stay with all who watched him play,” he said.
“On behalf of everyone at England Rugby, we extend our deepest condolences to Tom’s family, friends, and loved ones. Our thoughts are with them during this incredibly difficult time.”
