Reynolds had been in poor health for some months, The Guardian newspaper reported. Reynolds's son, Nick, a musician with the band, Alabama 3, with whom his father had occasionally performed, announced his death.
His death came just months before the 50th anniversary of the robbery.
In August 1963, a group of professional criminals from London robbed the Glasgow to Euston mail train in Buckinghamshire, England. The Guardian said they made off with off with 2.6 million pounds ($3.9 million), worth around 33 million pounds ($50 million) today.
Most of the robbers were caught and sentenced to what was then record sentences of 30 years.
But Reynolds fled the country and hid under an assumed name in Mexico and Canada with his wife and young son, the newspaper said.
He was when he returned to Britain in 1968. The Guardian said Tommy Butler, the detective who arrested him, greeted him by saying "Hello, Bruce, it's been a long time."
"C'est la vie," Reynolds replied.
Reynolds was jailed for 25 years, but wrote a book, "The Autobiography of a Thief."