Professional Darts Corporation chairman Barry Hearn told BBC Sport he collapsed at a Premier League event in Liverpool.
As news of his death reached the crowd at the Echo Arena, fans repeatedly sang: "There's only one Eric Bristow."
Hearn said Bristow, known by his nickname the Crafty Cockney, would "always be a legend in the world of darts and British sport".
World champion five times between 1980 and 1986, Bristow also won five World Masters titles and was a founder player when the PDC was formed in 1993. He was awarded an MBE for his services to sport in 1989.
He also worked as a TV pundit and appeared on ITV show I'm A Celebrity... Get Me Out Of Here in 2012.
From everyone at Mark Mardell we send out our condolences to his family and friends.