Tsvangirai pledged a new inclusive government that would find a new way of working, but warned that it would not provide an instant cure for Zimbabwe's problems.
"The partners in this new inclusive government cannot alone provide the solutions to the problems in this country," he said.
"All we can do, and will do, is to work together to establish the environment where every Zimbabwean has the opportunity to contribute to solve the problems we face."
The country's economic crisis, with inflation at more than 11 million per cent, the divisions between the three parties, and the legacy of the violence and intimidation during the elections were likely to be the major challenges for the new government.
Tsvangirai then looked uncomfortable as his new partner in government took to the stage to attack Britain, Zimbabwe's former colonial ruler, and the United States.
"African problems must be solved by Africans ... the problem we have had is a problem that has been created by former colonial powers," the 84-year-old president said.
"We must resist those who want to impose their own will on us."
However, he also pledged his commitment to the agreement, addressing Tsvangirai he said: "Let us be allies."
"People will want to see if what we promise is indeed what we strive to do ... We are committed, I am committed, let us all be committed."
Lance Guma, an exiled Zimbabwean and presenter with London-based SW Radio Africa, told Al Jazeera that he was very disappointed by Mugabe's speech.
"Mugabe's speech really was a big let-down, it was totally uncalled for ... he has nothing new to offer in the current set-up so all he can do is talk about history, all he can do is talk about colonialism," he said.
"I think his speech was an indirect response to Morgan Tsvangirai's speech where he was talking about doctors, teachers, food, cash availability and Mugabe felt he was being blamed for that.
Tsvangirai had called for Zimbabwe to be reopened to international aid.
"We need to unlock our doors to aid. We need medicine, food and doctors back in our country," he said. "We need electricity, water, petrol for our vehicles, we need to access our cash from banks."
"We need to unlock our doors to aid. We need medicine, food and doctors back in our country"
Zimbabwe prime minister
Al Jazeera's Haru Mutasa, reporting from Harare, said that Zimbabweans were cautiously optimistic about the deal.
"Generally people are glad that the election process is over and that something positive might come out of it," she said.
"They have been through a lot. There have been promises, promises that have not been delivered.
"They want the economy to be uplifted, they want jobs, they want their children to go to school, they want teachers to be paid well, they want basic services to be resuscitated, they are desperate, they are tired and once Morgan Tsvangirai is in power they hope he will work with Zanu-PF."
Mutumbara admitted that the government had to make "some very painful decisions to drive this country forward".
"We must make sure the healing is cascaded right from the top to the villages ... our country has gone through a painful experience and we have to heal from the top to the bottom."
Zanu-PF, the MDC and the smaller opposition grouping of Mutambara met in Harare on Saturday, agreeing to share out the 31 cabinet seats.
The powerful state security ministry was abolished while the justice portfolio was split into two and a new prisons department was formed.
The parties met again on Monday to allocate ministries, with the MDC reportedly pushing to take control of home affairs, local government, one of the justice ministries, information and finance.
The name of the individual heads of the ministries are expected to be announced later in the week, according to a government minister.