Mr Mugabe praised South Africa's President Thabo Mbeki, who helped broker the deal, but insisted that it would be Zimbabweans who resolved the crisis - without the influence of Europe or the US.
He has previously accused Mr Tsvangirai of being a puppet of Western powers - particularly the UK, Zimbabwe's former colonial master.
A US state department spokesman said it supported any talks that would lead to a result reflecting the "will of the Zimbabwean people".
UN Secretary-General Ban Ki-moon said he welcomed the deal and urged all sides "to engage, in good faith, in serious talks that would lead to a lasting solution".
Jean Ping, chairman of the African Union (AU), congratulated the parties on the deal and encouraged them to "build on this positive development".
New elections call
The MDC has previously accused Mr Mbeki of being biased in favour of Mr Mugabe.
Robert Mugabe speaks about signing the agreement
The fact that the AU and United Nations joined the South African mediation efforts was crucial in persuading the opposition party to agree to talks, analysts say.
Diplomats from the Southern African Development Community (Sadc) were also involved.
The MDC has set out several conditions to be met before starting substantive talks with Mr Mugabe, including the complete cessation of violence and the release of all political prisoners.
It wants some kind of "transitional authority" to organise new, internationally-monitored elections.
The MDC says at least 120 of its supporters have been killed, about 5,000 abducted and 200,000 forced from their homes since the first round of the elections, in a campaign of violence by pro-Mugabe militias and the army.
Cabinet ministers and military officials have denied the charges.
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