With all 10 provinces declared, Mr 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.
By narrowly winning more than 50% of the vote, Mr Mnangagwa avoids a run-off election against Mr Chamisa.
The president said on Twitter he was "humbled", and called the result "a new beginning".
Mr Mnangagwa, from the governing Zanu-PF party, took over as president last November from long-serving leader Robert Mugabe. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇