South Africa had been expected to win the vote after an independent review recommended they stage the tournament.
However, at a World Rugby Council meeting in London on Wednesday, France was chosen to hold the 10th event.
France - which was the main host of the competition in 2007 - won in the second round of voting, with 24 votes compared to 15 for South Africa.
Ireland, which staged matches in 1991 and 1999, was eliminated after getting eight of the 39 votes in the first round - France picked up 18 and South Africa 13.
South Africa hosted the World Cup in 1995, when the Springboks beat New Zealand 15-12 in the final.
World Rugby chairman Bill Beaumont described the selection process as the "most transparent and comprehensive" in the organisation's history.
"I am delighted for France. They have run a World Cup before and I think it will be an exciting World Cup," he said
Last month, South Africa had ranked highest in the independent review after the three bids were judged on five categories...
- vision and hosting concept
- tournament organisation and schedule
- venues and host cities
- tournament infrastructure
- finance, commercial and commitments
From the above criteria, South Africa scored 78.97%, France were second with 75.88% and Ireland were third with 72.25%, however members of the World Rugby Council opted to select France.
Japan will host the next World Cup in 2019.
'We cannot hide our desolation' - South Africa reaction
South Africa said they were "bitterly disappointed" at the decision, but would not appeal against the verdict.
"We would like to apologise to the people and government of South Africa for raising their hopes," added Mark Alexander, president of South Africa Rugby.
"We did everything in our power to bring the tournament to South Africa and we expected to have that right confirmed.
"We produced a compelling bid document that earned the unanimous recommendation of the Rugby World Cup Ltd board. That recommendation was questioned last week by rivals, but endorsed a second time by World Rugby last week.
"However, the view of the experts and World Rugby's leadership was overturned by World Rugby Council members, who may have had other factors to take into account.
"We cannot hide our desolation but, for the sake of rugby we wish the 2023 tournament hosts every success."
Chester Williams, who helped South Africa win the World Cup when they hosted the event in 1995.
He added: "It is a much needed event that we wanted here in South Africa and this could have been another opportunity for us as South Africa to reunite as a nation.
"It would have been an amazing opportunity to host the Rugby World Cup and the French have won it and we have to deal with it accordingly.
"We were about 90% certain that we would be hosting the World Cup. The whole of South Africa is going to be disappointed."
Other Rugby World Cup hosts
1987: Australia and New Zealand
1991: England (main hosts), Wales, France, Ireland and Scotland
1995: South Africa
1999: Wales (main hosts), England, Scotland, Ireland, France
2003: Australia
2007: France
2011: New Zealand
2015: England
2019: Japan
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