The Rail, Maritime and Transport union made the announcement "with the deepest regret".
A brief statement said: "It is with the deepest regret that RMT has to confirm that our general secretary Bob Crow sadly passed away in the early hours of this morning.
"RMT would request that all media respect the privacy of the friends and family of Bob Crow at this distressing time."
Mr Crow, who was 52, was one of the most high-profile, left-wing union leaders of his generation, sparking as much anger from passengers hit by rail and Tube strikes, as praise from his members for winning pay rises.
He was constantly involved in industrial disputes and campaigns and led a walkout by London Underground workers last month in a dispute over ticket office closures.
The straight-talking south Londoner was a passionate supporter of Millwall Football Club.
His death caused shockwaves in the trade union movement today.
Manuel Cortes, leader of the TSSA rail union, who stood on picket lines with Mr Crow during last month's Tube strike, said: "Bob Crow was admired by his members and feared by employers, which is exactly how he liked it.
"It was a privilege to campaign and fight alongside him because he never gave an inch."