His bandmates said they were "devastated" by the news about "our comrade, brother, founding UB40 member and musical legend".
They said he had endured a "long and heroic battle with cancer".
He had surgery to remove two brain tumours in 2019 and reportedly had another operation earlier this year.
Travers was a key part of the UB40 line-up as a saxophone player, arranger and lyricist.
The group, from Birmingham, found success in 1980 with Food For Thought, their first UK top 10 single, before having hits with I Think It's Going to Rain Today, One in Ten and covers of Red Red Wine and I Got You Babe.
In total, they have recorded 39 UK top 40 singles and 28 top 40 albums, and sold 100 million albums worldwide.
Travers formed the band with a group of school friends in the late 1970s, and the lack of jobs in the city led them to borrow the name of the official Unemployment Benefit Form 40, used by people signing on the dole.
"We had just signed on and somebody said 'UB40' and we all instantly knew that was the name of the band," Travers told The Telegraph in 2010.
"Thank God for the dole. We got fed, it paid the rent and it enabled us to concentrate on developing our careers. We commandeered a cellar and started rehearsing every day, nine till five.
"Our first experiences of playing an instrument started together, and we'd humiliate each other over mistakes. But we were very serious about our music."