The combination of Dublin-based Fyffes and America's Chiquita will create a group that may be able to squeeze better terms from retailers and suppliers.
With the enlarged group planning to retain the brands developed by the two firms, the oval blue labels used by Fyffes are set to remain a familiar sight in UK's shops.
Many of the bananas sold in Scotland are ripened and packed in a plant run by Fyffes in Livingston, where 110 people work.
The merger will create a firm that will be the biggest player in a group of giants that dominate the sector.
Fyffes and North Carolina-based Chiquita sell around 180 million boxes of bananas a year between them. The next ranked firms, Del Monte and Dole, sell 117 million and 110 million bananas a year respectively.
The new firm, to be called ChiquiteFyffes, will grab some 14% of the global banana market.
David McCann, Fyffes executive chairman, said: "This deal will be transformative and offer exciting opportunities for the new business. We are looking forward to working with the Chiquita team to build a combined company which is well positioned to succeed in our highly competitive marketplace and which will create significant value for our shareholders."
The deal will result in Fyffes surrendering its independence for a second time around 130 years after the banana trading operation was founded by a descendant of Henry and Nathaniel Fyffe, who ran a general trading business in Perth. This sold goods like buttons and tobacco before diversifying into tea trading.
Edward Wathen Fyffe started importing bananas to London in 1888. He had discovered the fruit while visiting the Canary Islands with his wife, Ida, in the hope she would find relief there from her tuberculosis.
After bananas became popular in the UK, the business was acquired by America's United Brands in 1913.
It was bought from United Brands by Fruit Importers of Ireland in 1986, then expanded rapidly at home and abroad by acquisition.
Fyffes bought James Lindsay, a leading Scottish fruit, flower and vegetable wholesaler, for £10.5m in 1990.
The combined ChiquitaFyffes will have $4.6 billion (£2.75bn) in annual revenues and expects to make operational pre-tax savings of at least $40 million (£24m) by the end of 2016.
Bananalink, a British-based group which works for more sustainable trade in bananas and pineapples, said: "Two big fruit companies have felt the downward pressure of the big retail buyers on their margins and consolidation appears to them to be a strategy for survival."
The new firm will be listed in New York, domiciled in Ireland for tax purposes and have a market value of $1.1bn (£661m). Chiquita shareholders will own about 50.7% of the combined company and Fyffes shareholders 49.3%.
The deal will be subject to review by competition authorities.
David Holohan, an analyst at Merrion Stockbrokers in Dublin, noted the two companies operate mainly in separate North American and European markets.
Chiquita shareholders will get one share of the new company for each share held. Fyffes investors will get 0.1567 of a share in the new group for each existing share, valuing it at a 38% premium over its Friday's closing price.