It is probably the most epic journey ever undertaken just to prove a point.
The established theory has always been that Polynesia was colonised via Asia around 5,500 years ago.
This has been backed up by archaeology, linguistics and some genetic studies.
But in 1947, Heyerdahl controversially claimed that Easter Island's famous statues were similar to those at Lake Titicaca in Bolivia, and sailed a raft from Peru to French Polynesia to prove it could have been colonised from America.
Now Professor Erik Thorsby of the University of Oslo in Norway has found clear evidence to support elements of Heyerdahl's hypothesis.
In 1971 and 2008 he collected blood samples from Easter Islanders whose ancestors had not interbred with Europeans and other visitors to the island.
Prof Thorsby looked at the genes, which vary greatly from person to person.
Most of the islanders' genes were Polynesian, but a few of them also carried genes only previously found in indigenous American populations.
Prof Thorsby found that in some cases the Polynesian and American genes were shuffled together, the result of a process known "recombination".
This means the American genes would need to be around for a certain amount of time for it to happen.
Prof Thorsby can't put a precise date on it, but says it is likely that Americans reached Easter Island before it was "discovered" by Europeans in 1722.
Prof Thorsby believes there may have been a Kon-Tiki-style voyage from South America to Polynesia.
Alternatively, Polynesians may have travelled east to South America, and then returned.
However, Prof Thorsby said that his new evidence does not confirm Heyerdahl's theory that the islanders were originally all from South America.
The first settlers to Polynesia came from Asia, and they made the biggest contribution to the population, he said.
"Heyerdahl was wrong but not completely," he said.
The work was presented at a Royal Society talk in London and reported in the New Scientist.