The merged company will maintain the brands of each company.
Generations of Americans know Chiquita brand bananas, brought to life in 1944 by the glamorous Miss Chiquita animated banana and portrayed live by models and personalities.
Fyffes has extended its ground-breaking oval Blue Label banana brand to Blue Label Pineapples and winter season melons.
The combined company will be listed on the New York Stock Exchange and based in Ireland.
Chiquita, based in Charlotte, North Carolina, posted a loss of $16 million for 2013, a sharp improvement after losing $405 million in 2012.
On Monday, Fyffes announced preliminary results for 2013 showing a profit of 26.1 million euros ($34.87 million), up almost 10% from the prior year.
Chiquita shares jumped 12.1% to $12.15 in late-morning trade in New York. Fyffes soared 42% to 106.50 pence in London.
Copyright Agence France-Presse, 2014