Electoral officials said turnout at Monday’s vote averaged 75 percent.
“It is our view that the high voter turnout is indicative of the sound voter education and publicity conducted on a receptive electorate,” Priscilla Chigumba, electoral commission chief, told reporters in the capital, Harare.
More than five million people registered to take part in the closely contested elections.
The electoral body said 90 percent of the polling stations had opened on time by 8am local time (05:00 GMT).
In the capital, Harare, long queues of voters were formed for several hours prior to the opening of the polls, before easing by mid-afternoon. Polls closed at 17:00 GMT.
Twenty-three candidates are competing for the presidency, with incumbent President Emmerson Mnangagwa, 75, of ZANU-PF facing stiff competition from the youthful Nelson Chamisa, the 40-year-old leader of the Movement for Democratic Change (MDC).
Previous elections in Zimbabwe were marred by intimidation and threats but campaigning and voting this time have been relatively peaceful.
For the first time since 2002, election observers from the European Union and United States were allowed to monitor the process.
Elmar Brok, the EU‘s chief observer, told Al Jazeera that voting went smoothly in some cases but was disorganised in others.
“We have seen cases where people waited for six hours because of bad organisation,” he said from Harare.
“We have seen this in urban areas, in the poor neighbourhoods. We have to check whether that’s organised in a certain way or that’s the way because of the huge amount of people that came.”
Brok said “there was a lack of transparency in the preparation of the elections”, citing the voters’ list.
“Also, there was unfairness in the public media in the time of the elections and we have to check whether that had impact on the final outcome of the elections.”
He added, however: “If I compare it to past elections, it is a progress.”
Meanwhile, the regional body – the Southern Africa Development Community (SADC) – said it was satisfied with the Monday’s voting process.
“So far the elections are going well. The voting has been taken, generally, in a peaceful environment and [an] orderly manner,” Manuel Domingos Augusto, Angola‘s external affairs minister, who is part of SADC’s election observation mission, told Al Jazeera.
“We must congratulate, in advance, the people of Zimbabwe. It looks like it will be a free and fair election,” he added.
Earlier in the day, both Mnangagwa and Chamisa were optimistic and promised to deliver change.
“This country is enjoying democratic space which has never been experienced before,” Mnangagwa said after casting his vote in the central city of Kwekwe.
For his part, Chamisa went a step ahead.
“I have no doubt by the end of the day here, we should be very clear as to an emphatic voice for change. And I represent that,” Chamisa said after voting in Harare, surrounded by enthusiastic supporters.
A presidential runoff will be held on September 8 if a candidate does not secure more than 50 percent of the votes.
Official results are expected to be released by Saturday.
Parliamentary and local elections are also taking place in the southern African country.