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The event for cars, trucks and motorcycles will take place in Argentina and Chile from Jan. 3 to 18, a spokesperson for the French organisers Amaury Sport Organisation (ASO) said.
Details on next year's race will be announced later. The organisers did not say whether the event's name would be changed.
The Dakar Rally, originally known as the Paris-Dakar, had always been staged entirely or mostly in Africa in its 30-year history.
It was cancelled for the first time last month due to security concerns in Mauritania where four French tourists were killed by suspected al Qaeda rebels in December.
Organisers had been advised by the French government to cancel the race because of a "terrorist risk" in Mauritania.
"We are not really surprised. We were expecting this decision, even if it's true that we have lost a great opportunity to show the world our cultural heritage," Mauritanian Tourism Minister Madine Ba told Reuters.
"This trail through the desert is enjoyed by many people and I'm sure other competitions will take up the baton. We've already been in contact with other rally organisers."
Government officials have estimated the loss of the rally will cost Mauritania, an Islamic Republic straddling black and Arab West Africa, 3.6 million euros ($5 million) this year alone.
Officials in neighbouring Senegal, from whose capital the rally takes its name, also said they were unsurprised by the decision not to hold the competition in Africa next year.
"We hope that as soon as the security conditions allow, the Dakar Rally will return to its source," Dialo Kane, president of the Senegalese motor sports federation, told Reuters.
"A lot of competitors take part because of their love of Dakar and of the African continent."