"It is with deepest regret that we have to announce the very sad news that our much loved husband and father John 'Brad' Bradbury passed away on Monday," his family said.
The band split up in 1981 and he joined the re-versioned group, The Special AKA, and stayed through to their dissolution in 1984. He was on board when The Specials reformed in 2008.
The Specials (from left) Terry Hall, Horace Panter, Neville Staple, Lynval Golding, the late John Bradbury, who passed away Monday, and Roddy Byers, pose for a photo at an awards ceremony in 2009.
"He was much respected in the world of drumming and his style of reggae and ska was seen as genuinely ground-breaking when The Specials first hit the charts in 1979."
Tributes from friends and fans flowed on social media.