Berwickshire-based Produce, a major wholesaler of potatoes itself, is paying £11m while also issuing £4m of new shares.
Alongside that it has raised £6m through a share placing which will help to part fund the acquisition.
The remainder is coming from existing cash resources and an extension of banking facilities with HSBC.
The transaction, which was first mooted in January this year, further involves an option for Produce to buy Peacock Farm, which owns the freehold property of Jersey Royal's main packing site on the island of Jersey, for a price of £6.35m within three years.
The Kent Potato Company, which is owned by Jersey Royal, is also part of the deal. In 2013 the entire Jersey Royal business had revenue of more than £31m but made a pre-tax loss of around £100,000.
Produce, which has its main base at Duns and employs 250 people in Scotland, said it expects the deal to enhance its earnings from 2015.
Barrie Clapham, chairman of Produce, said: "I am delighted we have been able to purchase such a well-known business.
"It takes the company into a very significant sector of the potato market and we are both excited and confident about the future earnings potential.
"This acquisition marks an exciting period for Produce Investments and the employees at both [Jersey Royal Company] and [Kent Potato Company], providing an opportunity to continue to develop a business which combines real food and farming heritage with the demands of modern supply chains and consumer passion for this high-quality brand."
The Jersey Royal Company employs 500 staff at peak times and produces around 25,000 tonnes of potatoes annually. They are grown by 20 farmers over 1,800 hectares of land on the Channel Island.
Jersey Royals are favoured by chefs and known for their distinctive taste, which is created by the soil and growing conditions on the Channel Island.
The potato is thought to be the only fresh fruit or vegetable in the UK to enjoy EU Protected Designation of Origin status, owing to the way it is grown, cultivated and harvested.
Separately, Produce confirmed its packing plant in Shropshire, which employs around 190 people, will close in August.
It said the volumes from that site will transfer to the Scottish Borders and Cambridgeshire.
Previously it indicated that would create around 50 jobs.