With all 10 provinces declared, Emmerson Mnangagwa won 50.8% of votes, compared to 44.3% for opposition leader Nelson Chamisa.
Police removed opposition officials from the electoral commission stage when they rejected the results.
The chairman of Nelson Chamisa’s MDC Alliance said the count could not be verified.
By narrowly winning more than 50% of the vote, Emmerson Mnangagwa avoids a run-off election against Nelson Chamisa.
Emmerson Mnangagwa, from the governing Zanu-PF party, said on Twitter he was “humbled”, and called the result “a new beginning”.
He took over as president in November 2017 from long-serving leader Robert Mugabe.
Nelson Chamisa has insisted he is the winner of the presidential poll, telling reporters on August 2 that Zanu-PF was “trying to bastardize the result”, something “we will not allow”.
However, the Zimbabwe Electoral Commission (ZEC) said there was “absolutely no skullduggery”.
Six people died after opposition protests in Harare on August 1 over alleged vote-rigging.
The elections were the first since former President Robert Mugabe, 94, was ousted and were intended to set Zimbabwe on a new path following years of repressive rule.
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