Their study effectively dismisses one of the most popular theories about the outbreak's origins - that it was brought over by football fans.
The findings, published in the journal Science, suggest the virus arrived between May and December 2013.
That is long before any cases were first detected in 2015.
The other popular idea - that it was brought over during the World Sprint Championship canoe race in 2014 - has also been dismissed.
Case zero
Tracing the origins of a virus takes a feat of genetic genealogy.
The researchers analysed the genetic code of seven Zika samples from across Brazil.
First, they discovered all of the viruses were closely related, suggesting the infection was brought to Brazil by just one person.
The virus has since spread to 34 countries or territories.
But Zika is still a virus that mutates rapidly. The small differences between each sample allowed the scientists to construct Zika's family tree and estimate when their common ancestor arrived in Brazil.
They conclude that the virus was brought over in mid-to-late 2013.
Prof Oliver Pybus, from the University of Oxford, told the BBC News website: "We can't be sure exactly how the virus got into the Americas, but it certainly seems that the virus was already in the continent before the start of the World Cup in 2014.
"We also looked at the numbers of passengers embarking from countries that have recorded Zika transmission in the last few years and who disembarked in Brazil and we found a 50% rise in the number of passengers along those routes. That could be a reason why it appeared when it did."
The virus spreading in the Americas is closely related to the one detected in an outbreak in French Polynesia in 2013.
While this is a possible source of the latest outbreak, the researchers say a lack of samples from other countries - particularly in south East Asia - mean they cannot be sure.
Microcephaly
One of the most disturbing aspects of the outbreak has been the strongly suspected link with a surge in cases of microcephaly - babies being born with small brains.
Dr Nuno Faria, a fellow researchers at the Evandro Chagas Institute, said their data was "consistent" with suggestions that Zika could be causing brain defects.
But he cautioned there was still more research to be done to confirm the link and "we will have a much better picture of the virus later this year".
Their analysis did not discover any major mutations in the virus that could make it more dangerous to developing brains.
The scientists suggest co-infection with other diseases such as Chikungunya, previous infections with Dengue or a lack of immunity could explain the spike in birth defects.
Commenting on the findings, Prof Martin Hibberd from the London School Of Hygiene and Tropical Medicine, said: "The introduction of one Zika virus leading to a widespread outbreak may seem surprising.
"However the modelling of other Zika outbreaks, and also the highly-related Dengue outbreaks, suggests that this is not unusual.
"In the right conditions, with sufficient mosquitoes and closely packed humans, the virus can spread rapidly."
Source: BBC
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