They say that inscriptions on a cylinder-shaped seal and fragments of a plaque indicate that the Olmec people used a form of words in about 650BC.
That is about 350 years earlier than the writings accredited to the Mayan civilisation who had been thought to have written the first words in the Americas.
The new findings, published by Science magazine, focus on the word-pictures or glyphs found on the artefacts unearthed near La Venta, a known centre of the Olmec civilisation.
Anthropologist Mary Pohl, from Florida State University, said it made sense that the Olmec had a form of writing as they had developed other traditions such as urban settlement and monumental architecture.
"Since the Olmec were the first to put together a political state, and writing is closely related with rulers in terms of publicising their power, it makes sense that they would be the first to use a system of writing," she said.
Ms Pohl led a research team during investigations in 1997 and 1998 and then the lengthy analysis of their finds.
Signs of power
One of the inscriptions on the seal contains the symbol "3 Ajaw", which the archaeologists believe to be the name of a day in the Olmecs' 260-day calendar, and possibly also the name of a king.
The scientists suggested that the cylinder seal could have been used to imprint the name "3 Ajaw" on noblemen's clothing to signify their links with the centre of power.
Ms Pohl said: "Clothes and jewellery were important items of display to show your rank and status, so it would show you were part of the elite to be able to display your connection to the ruler."
Some of the symbols could not be translated, but the researchers say they are similar to glyphs seen in texts from the later Mayan culture which become dominant in the area.
They suggest that writing spread from La Venta to other regions and that the Maya, whose culture flourished from 300AD to 900AD, eventually developed the Olmec system into the most sophisticated script in pre-Hispanic America.
The Olmecs were one of the earliest civilisations to establish themselves in the Americas, at first in southern Mexico and later Guatemala.