"The SADC has decided and we are bound by that decision."
He added that Zanu-PF had made "significant concessions", saying that the MDC would continue the struggle for a democratic Zimbabwe in a new arena.
Mr Mugabe's supporters welcomed the decision.
"We are obviously happy as Zimbabweans that we are now able to focus on reconstructing our country and move away from politicking all the time," Information Minister Paul Mangwana told the BBC.
"This is a glorious opportunity for Zimbabweans to work together and show the whole world that we are able to solve our problems on our own."
A statement by South Africa's foreign ministry, quoted by AFP, welcomed the move, saying it would "help lay the foundation for the people of Zimbabwe to begin to address current challenges facing their country".
Meanwhile UK Foreign Secretary David Miliband said the new government would be judged on its actions.
"The international community will be looking for the government to demonstrate, through its actions, a clear commitment to reform," he said.
But US State Department spokesman Robert Wood said Washington was "a bit sceptical" about the deal.
"What's important here is actions and not words, and we want to see real, serious power-sharing by the Mugabe regime. So I think the jury is still out on this one," he said.
The BBC's Southern Africa correspondent Peter Biles says that agreeing to the deal requires a leap of faith for the MDC, which has no trust in Mr Mugabe.
But the decision to commit itself was the only realistic option short of abandoning plans for a unity government, he says.
SADC's POWER-SHARE TIMELINE
5 Feb: Zimbabwe to pass power-sharing constitutional amendment
11 Feb: PM-designate Tsvangirai and his deputies to be sworn in
13 Feb: Remaining ministers and their deputies to take office
The disagreements centred on how the most powerful cabinet posts were to be shared out, and on the MDC's insistence that attacks on its members should stop.
Observers say the MDC now appears to have adopted a strategy proposed by SADC leaders that it should first enter the government and then resolve outstanding issues.
The wrangling over power-sharing has paralysed Zimbabwe's government for months.
Mr Mugabe's Zanu-PF and the MDC have also started setting up a joint committee to monitor the power-sharing pact.
It will deal with any breaches in the power-sharing deal and could also address concerns the MDC may have about the arrest of party members and activists.
South African President Kgalema Motlanthe, who chaired an emergency summit this week to get a deal, said the MDC was committed to a timeline agreed by the parties.
"...[Mr Tsvangirai] is going to be chairing cabinet and also sitting in the national security council...," he said.
"We believe that this is a transitional authority essentially and its primary task is to achieve stability and the economic recovery of that country."
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