The new firm, named ChiquitaFyffes, is expected to sell about 160 million boxes of bananas annually, more than any rival firm.
"This is a milestone transaction for Chiquita and Fyffes that brings together the best of both companies," said Chiquita boss Ed Lonergan.
It will be listed in New York.
The merger will see shareholders receive shares in each firm, with Fyffes shareholders owning about 49.3% of the combined company.
Mr Lonergan said the deal would help it to save costs and expand the areas it served.
The tie-up came as Fyffes revealed that its profit before tax for 2013 rose 9.8% to 28.7m euros (£23.8m).
It said results in its banana division were "broadly satisfactory", although profits in that division were slightly down compared with 2012's strong performance.
It said "significant inflation" in the cost of fruit and the strength of the US dollar against sterling had both hit performance.
