Al Jazeera's Haru Mutasa said that people in Harare, the Zimbabwean capital, were relieved that the impasse was over.
"The country has been in limbo for a long time economically - people just wanted this over and done with.
"The question is how much power has the leader of the opposition been given. He wanted more of a say in the running of the country."
Mugabe, 84, won a controversial June presidential runoff unopposed after Tsvangirai withdrew, citing state-sponsored violence against his supporters.
Tsvangirai had won the first round of the presidential election in March, but fell short of an absolute majority.
Mugabe has led Zimbabwe since independence from Britain in 1980, but his party lost its parliamentary majority to the MDC for the first time in legislative elections in March.
While the political crisis has dragged on, Zimbabwe's economy has continued its freefall with the world's highest inflation rate - 11.2 million per cent in June, according to official figures.
Once hailed as Africa's breadbasket, Zimbabwe's economy has virtually collapsed over the past decade with inflation out of control and chronic shortages of foreign currency and food including the staples cornmeal, sugar and cooking oil.