Zimbabwe's electoral commission says it expects to start announcing election results from 3 p.m. (1300GMT) on Tuesday.
Africanews journalist Nyasha Mutizwa is from Zimbabwe and she's has been following up on the polls with our men on the ground.
She said she was confident there was no "cheating" and that the commission will respect the will of Zimbabweans: "We will not steal their choice of leaders". If no presidential candidate wins more than 50 per cent of the vote, a runoff will be held September 8.
"I am delighted by the high turnout and citizen engagement so far", Mnangagwa tweeted.
The election commission has denied any allegations of vote rigging and said it had five days to release the results. Opposition leader Nelson Chamisa has said he would lead peaceful protests if the vote is found to be flawed.More news: Lunar Eclipse July 2018
Chamisa, a lawyer and pastor who leads the opposition Movement for Democratic Change party, has gone further, saying his own count shows that he won the election and that he's ready to form the next government.
Under Mugabe, elections were often marred by violence, harassment and irregularities.
Zimbabweans were also electing 210 members of parliament and more than 9,000 councillors.
"Concerns still remain about the independence of the ZEC amid executive interference in key electoral processes", Andrew Makoni, the chairman of the network, which deployed about 6,500 observers, said in Harare on Tuesday. The election was the first since longtime leader Robert Mugabe stepped down in November under military pressure and former confidante Emmerson Mnangagwa took power. "He is young and can understand our plight as youth", said Ndumiso Nyoni, 20, a worker at a lodge in Lupane, southern Zimbabwe.
A voter in Harare, the capital, said Zimbabwe is anxious to hear the election results as soon as possible. "Because people are not yet settled, they're thinking of too many things. People are looking for that".