Researchers made the prediction after conducting an audit of more than half a million museum specimens collected from the Amazon between 1707 and 2015.
They ended up with a list of 11,676 different tree species. Based on this figure, they believe about 4,000 of the rarest Amazonian trees remain to be discovered and described.
Conservationist Dr Nigel Pitman, from the Field Museum in Chicago, US, said: “Since 1900, between 50 and 200 new trees have been discovered in the Amazon every year.
“Our analysis suggests that we won’t be done discovering new tree species there for three more centuries.”
In 2013 scientists guessed there were around 16,000 tree species in the Amazon.
The new study, published in the journal Scientific Reports, suggests this estimate is probably a good approximation.
It was made possible by the digitisation of museum collection data - photos and records of specimens that can be shared online by experts around the world.
The species list will assist those trying to preserve the rainforest in the future, said the scientists.