The former prime minister had reportedly been suffering from colon cancer.
"He died this evening. The family communicated this to me," MDC vice president Elias Mudzuri told Reuters.
Mr Tsvangirai had been suffering from colon cancer for at least two years, but his condition deteriorated rapidly in recent days despite treatment in neighbouring South Africa.
His death will be an enormous blow to the opposition in Zimbabwe, coming only months before the first elections were due to be held in the former British colony since the end of Robert Mugabe's near four decade rule last year.
He had a tumultuous and era-defining career in Zimbabwean politics.
Mr Tsvangirai's illness was said to have divided the MDC (Movement for Democratic Change), with some party officials reportedly jockeying to succeed the former trade union activist.