Dida, a former high school teacher and presidential candidate, added that Tsvangirai stood against the dictatorial leadership of Mugabe and was principled.
Tsvangirai, 65, who had been battling cancer since 2016 died at a Johannesburg hospital where he had been receiving treatment.
The opposition party's acting president Engineer Elias Mudzuri announced the death of the opposition leader in a South Africa hospital a few minutes ago.
"We have lost our icon and fighter for democracy", said Mr Mudzuri.
Mnangagwa has abolished 51% black ownership requirements for miners other than diamond and platinum, and has said he would step down if he lost the election to be held later this year.
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"Go well and rest in power, Morgan Tsvangirai". In 2000 the MDC rattled Mugabe's Zanu-PF by coming within a few seats of beating it in parliamentary elections.
In 2013, comfortable in a state home, Tsvangirai seemed to have overplayed his hand. "Had it not been for his leadership and his determination, I think we would have been stuck with our old constitution".
"The ANC expresses its condolences to the family of Morgan Tsvangirai and all supporters of the MDC", it said.
Zimbabwe's main opposition leader, Morgan Tsvangirai, passed away on Wednesday.
Mr Tsvangirai's death was confirmed to The Telegraph by a family member.
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Tsvangirai was born on 10 March 1952 in the Gutu area of Southern Rhodesia, one of nine children of a carpenter.
In a statement, Mnangagwa said that the late veteran opposition leader would be remembered for his "readiness to stretch and reach out across the political divide for a government of national unity after the polarising 2008 elections".
The eldest of nine children, Tsvangirai worked at a textile mill in Mutare in the east, and later joined a nickel mine in Bindura, a town in the country's north.
Tsvangirai became involved in union activities and was elected to the executive of the National Mine Workers Union.
The course of Tsvangirai's life was determined by his long political battle against Robert Mugabe, the former guerrilla leader who had run Zimbabwe since independence from Britain in 1980 until November 2017.
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