Mr Tsvangirai won the first round of last year’s presidential election – but he withdrew from the run-off citing violence against his supporters.
However he later agreed to share power with Mr Mugabe.Problems facing the new government include a cholera epidemic, a collapsed economy and a 90% unemployment rate.
Mr Mugabe administered the oath to Mr Tsvangirai in a ceremony in Harare.
The new prime minister faces formidable challenges.
More than 3,400 people have died in Zimbabwe’s cholera epidemic, and the country has stopped publishing figures, amid hyperinflation, and people use foreign currency wherever possible.
More than half the population rely on emergency food aid.
The cabinet in the new coalition government will be sworn in on Friday.
The tasks facing the ministers are daunting and there is deep scepticism about whether it will work, says the BBC’s southern Africa correspondent, Peter Biles, in Johannesburg.
At best it will be a transitional arrangement leading eventually to a new constitution and fresh elections, he says.
On Tuesday, Mr Tsvangirai named Tendai Biti, the secretary general of his Movement for Democratic Change (MDC), as his choice for finance minister.
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A Zimbabwean judge last week dropped treason charges against Mr Biti over an alleged coup plot, citing lack of progress in the case against him.
Mr Biti’s new position will be a key one, given the country’s economic collapse.
In January, Mr Tsvangirai returned to Zimbabwe after an absence of more than two months for fresh talks with Mr Mugabe on sharing power.
Earlier negotiations had faltered after the MDC accused Mr Mugabe’s Zanu-PF of keeping the most powerful ministries – including the one that controls the police – to itself.-BBC