Tsvangirai, who founded the Movement for Democratic Change (MDC) in 1999, was among the most prominent critics of Mugabe, the long-time authoritarian leader who was ousted from power in November.
"It is sad for me to announce that we have lost our icon and fighter for democracy," Elias Mudzuri, one of the vice-presidents of the MDC, said on Twitter.
Tsvangirai's death was confirmed to AFP by another senior party member. He was 65.
Mugabe's government detained him on numerous occasions over his vocal criticism of the regime.
Security forces swooped on Tsvangirai in 1989 after he bluntly warned about the rising tide of political repression in the country.
Tsvangirai also claimed to have been the target of four assassination attempts -- including one in 1997 in which he said attackers attempted to throw him out of his office window.
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