Mugabe, who has been in charge of the country since it gained its independence from Britain in 1980, and Tsvangirai, leader of the Movement for Democratic Change, signed an agreement in September to a power-sharing government, but bitter political wrangling since then put the agreement in doubt.
Zimbabweans watched on state television as Tsvangirai raised his right hand during a brief ceremony and said, "I will well and truly serve Zimbabwe in the office of prime minister of the Republic of Zimbabwe, so help me God."
Tsvangirai's deputies Arthur Mutambara of a breakaway opposition party and Thokozani Khupe of Tsvangirai's party also were sworn in, according to the Associated Press.
The coalition agreement calls for the government to make economic revival its priority. An exorbitant inflation rate has left millions of Zimbabweans dependent on international food aid, and a crumbling health and infrastructure system has caused a cholera outbreak that has killed at least 3,400 people since August, according to the U.N. World Health Organization.
Mugabe and Tsvangirai have been at odds since the opposition group posed the most serious threat to the ruling regime since the country's independence.
Tsvangirai won a first round presidential poll against Mugabe in 2008 but boycotted the subsequent runoff over violence and Mugabe emerged the winner.
"We must get the country working again," Tsvangirai said in his inaugural address.
He said civil servants would be paid in foreign currency instead of the increasingly worthless local currency, but he did not say where the money would come from, Reuters reported.