A run-off vote is scheduled for September 8 if no presidential candidate wins at least 50 percent.
A credible vote is key to lifting global sanctions and attracting foreign investment to revive Zimbabwe's shattered economy.
A credible vote is essential if Zimbabwe is to exit painful sanctions and secure the donor funding and investment needed to stem chronic cash shortages.
In his first major statement since being ousted by the military last November, Mugabe told reporters in Harare he would be voting for the Movement for Democratic Change (MDC), the country's biggest opposition party, and its candidate Chamisa.
Chamisa, a charismatic speaker who honed his craft in the courtroom and the pulpit, has won over young and unemployed voters who are frustrated with almost four decades of Zimbabwe African National Union-Patriotic Front (ZANU-PF) rule.
Dozens of people waited in line to vote outside many polling stations in Harare, the capital. "The president is here!" We removed Mugabe and they came to support when we said Mugabe must go.
He has promised to rebuild the country's devastated economy, but been criticised for making extravagant promises - such as the introduction of a high-speed bullet train and bringing the Olympics to Zimbabwe. I mean, they are just perpetuating their bias.
View Slideshow A sign hangs from the train station roof in Bulawayo. Claire Harbage NPR
Some voters were being turned away at polling stations as their names were not captured on the voters roll, even though they claimed to have registered and received registration slips. What began with optimism crumbled into repression of the opposition, alleged vote-rigging, violent land seizures from white farmers and years of global sanctions.
Zimbabwe has moved on from former president Mr Robert Mugabe's authoritarian rule and the nonagenarian must know that he does not hold sway over the majority of the people, war veterans and political analysts said yesterday.
"I never thought (Mnangagwa) would be the man who turned against me", he added. Zanu-PF and its leader will win this election because they have the support.
The elections have been opened up to worldwide observers, though the opposition has voiced concerns that the voter roll has irregularities and claimed that the army has been deployed to rural areas in an attempt to intimidate people to vote for the ruling ZANU-PF. Tsvangirai pulled out of the second round vote in an effort to end the bloodshed.
Mnangagwa has welcomed in foreign media and global observers from the European Union, the United States and the Commonwealth, who are watching polling stations across the southern African country. I have to see a better Zimbabwe for my kids.
While Zimbabweans are deciding who to choose, the United States is struggling to influence a country whose economy has seen significant investment from China.
Mnangagwa, often referred to as just "ED", has made a big effort to win over the worldwide community; hosting Western ambassadors, courting foreign investors and even patching up relations with white commercial farmers who were violently evicted from their farms under Mugabe. "My main concern is the Zimbabwe Electoral Commission, it obviously has a preferred party", he said.