Sainsbury's boxes will go on trial at the end of August in Anglia and the East Midlands and Tesco will launch in early September in the South London area.
A typical box from Sainsbury's will contain eight varieties of seasonal produce and cost under£15. Tesco plans to change its selection of fresh fruit and vegetables fortnightly. Both will include the information about the individual farms where the goods were sourced.
Sainsbury's said it aims to support local suppliers, but will source goods nationwide in order to maintain consistency. The group said it would never include imported goods in an organic box.
The supermarket has also suggested that it could extend the scheme to cover organic meats if the vegetable boxes are successful.
Data from AC Nielsen showed sales of the Sainsbury's So Organic range were up 18.4 per cent year on year for the 52 weeks to July 3. Sainsbury's market share of the organic market stands at 30 per cent.
The organic food market is worth£1.6 billion a year and growing at 30 per cent a year.