Mr Hichilema defeated the incumbent, President Edgar Lungu, by a landslide - more than a million votes.
It was Mr Hichilema's sixth attempt at winning the presidency. His supporters have been celebrating on the streets of the capital, Lusaka.
Mr Lungu has accepted defeat and congratulated Mr Hichilema.
Earlier, he alleged that the elections were not free and fair and said ruling party election officials had been chased from polling stations, leaving votes unprotected.
In its final tally, the electoral commission said Mr Hichilema had won 2,810,777 votes to Mr Lungu's 1,814,201 in Thursday's election. There were seven million registered voters.
"I therefore declare that the said Hichilema to be president of Zambia," commission chairman Esau Chulu announced at the results centre in Lusaka.
Mr Lungu's six-year rule was criticised for alleged human rights abuses, corruption, a failing economy and massive unemployment.
Correspondents say Mr Hichilema, 59, tapped into widespread dissatisfaction among voters.
He now faces the daunting challenge of turning around the country's economic fortunes.
Celebrations which started on Sunday continued until sunrise as Zambia was painted red by supporters of Hakainde Hichilema.
There's no doubt that that political winds of change were ushered in by young people who are often accused of being reluctant to vote. They turned up in high numbers and generally rejected President Edgar Lungu.
"We want jobs, young people want jobs," chanted throngs of people as they filled the streets of the capital shortly after Mr Hichilema was declared the seventh president of this copper-rich nation.
There's no doubt that Mr Hichilema will inherit the rot and will attempt to clean up corruption left by his predecessor.
Who is Hakainde Hichilema?
He managed to get a scholarship to the University of Zambia, and later graduated with an MBA degree from the University of Birmingham in the UK. He went on to become one of Zambia's richest men, with business interests in finance, ranching, property, healthcare and tourism.
Hakainde Hichilema addresses a media conference in Cape Town, South Africa, August 31, 2017
Mr Hichilema has described himself as an ordinary "cattle boy" and has contested and lost every election held in Zambia since 2006. However, each time he has increased his share of the vote.
In 2016, Mr Hichilema said the election was stolen from him after he lost to Mr Lungu by just 100,000 votes.
Mr Hichilema has faced problems with authorities since entering politics.
After the 2016 election, he was charged with treason for allegedly failing to give way to the presidential motorcade. He spent four months in a maximum-security jail before the charges were dropped.