The proposed new business will be called ChiquitaFyffes and generate revenues of 4.6 billion US dollars (£2.75 billion) from the sale of more than 160 million banana boxes a year, as well as melons and pineapples.
Dublin-based Fyffes, which also sells products under the Sol brand, employs more than 12,000 people worldwide. Chiquita is the larger of the two firms with annual revenues of 3 billion US dollars (£1.8 billion) and 20,000 staff.
Shareholders in the North Carolina-based company will own 50.7% of the combined business following the merger, which values Fyffes at 526 million US dollars (£314.5 million).
The existing brands will be retained but customers will have access to a more diverse product mix and choice, the two companies said.
Fyffes executive chairman David McCann, who will become chief executive of the merged business, said: "Our outstanding employees will benefit from working for a larger, more diverse business which offers opportunities for growth.
"We believe we will be able to use our joint expertise, complementary assets and geographic coverage to develop a business that can run smoothly and efficiently to better partner with our customers and suppliers."
Fyffes began trading in the 1880s when the first commercial delivery of bananas from the Canary Islands arrived in London for EW Fyffe, Son & Co.
The world's oldest fruit brand came into being in 1929 with the famous blue label and its bananas are sourced in the Tropics from countries such as Costa Rica, Guatemala and Colombia.
It currently employs about 4,000 people in the UK and Ireland, including in Portsmouth, Livingston and Wakefield.
The new company, which is valued at one billion US dollars (£601 million), will be listed on New York Stock Exchange and domiciled in Ireland.
Fyffes generates 81% of its revenues from the sale of bananas, with 12% coming from melons and the rest from pineapples. Around a third of Chiquita's revenues currently come from salads and healthy snacks.
The combined company will generate 47% of its revenues from the United States and 46% from Europe. It will be the largest player in the European banana market and second largest in the United States.
Fyffes also announced annual results today, with underlying profits up 6.9% on a year earlier to 32.7 million euros (£27.3 million).
It said it achieved a "broadly satisfactory performance" in the banana category, even though profits were slightly down on a strong result the previous year.
Mr McCann said: "The industry experienced further significant inflation in the cost of fruit during 2013, continuing a multi-year pattern.
"There was also an unfavourable movement in exchange rates year on year, due to the strength of the US dollar particularly relative to sterling."