The ballot counting started immediately after the voting ended on Wednesday night.
Election officials said that a few polling stations remained open into the night to allow those already arriving at closing time to cast votes.
Rita Makarau, the head of the election commission, told a news conference in the capital Harare that exit polls were expected to come out early Thursday.
Final results are expected by Monday and if no candidate receives over 50 percent of the votes, a runoff will be held, most likely in September.
Makarau also pointed out that the vote was free and fair, with no reported violence.
“I believe that the election is free and fair,” she said, adding, “Maybe the reports that will come out will vindicate my view of the election as free and fair.”
African Union (AU) observers have also described the voting as “orderly and peaceful.”
Some 6.4 million people, or half of the Zimbabwean population, were eligible to cast their ballots at 9,670 polling stations across the African country.
Five presidential candidates are competing in the race. Long-time President Robert Mugabe and Prime Minister Morgan Tsvangirai are the main rivals, with both having predicted landslide wins.
Mugabe and Tsvangirai have been sharing power since 2009, following a deal brokered by a regional bloc to end the unrest sparked after 2008 election.
Violence broke out in the last presidential election in 2008, forcing Tsvangirai out of the race despite a first round win after 200 of his supporters were killed in the unrest.