Tsvangirai's body arrived in the capital, Harare, on Friday and was taken to a military barracks where it will remain until Monday for public viewing.
AFP reports that Zimbabwean President Emmerson Mnangagwa praised Tsvangirai as an outstanding political figure who had endured political hardship and deserved his place in history.
The President urged Zimbabweans to remain united ahead of elections due by July this year.
Tsvangirai's prominence across Africa as a veteran opposition leader was highlighted by the visit to Zimbabwe of Kenyan opposition leader Raila Odinga.
Addressing mourners at the former prime minister's Harare home Sunday, Mnangagwa said the government would pick up the tab for his treatment at the private Johannesburg clinic.
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Before being forced into a power-sharing deal with ZANU-PF as a prime minister, Tsvangirai was beaten up by police, his rallies were banned and he was charged with treason and jailed.
Tsvangirai pulled out of an election run-off in 2008 following violence which, he said, claimed the lives of at least 200 of his supporters.
The opposition party once posed the sternest challenge to former leader Mugabe and his ruling ZANU-PF party since the southern African nation's independence from white minority rule in 1980.
Fungai Nyapopoto, 40, a street vendor who travelled to pay his respects, said: "I am mourning our great hero, a man of the people. We will always remember him".
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