The shops are located in Hampshire, Wiltshire, Somerset and Cornwall, with completion for the takeover scheduled for the end of September.
Greenstead and RNS are two separate companies, owned by the same family firm. At present 11 of the stores trade as Spar and three as Nisa. Six of the stores also have Post Offices, which will be retained.
Southern Co-operative said the stores, which range in size from 1,500 to 3,000 sq ft, will continue trading without interruption throughout the takeover.
A spokesman for the GD/RNS group said: "As the industry becomes increasingly competitive, we thought it best to become part of a bigger and better-resourced operation to take the business forward."
Graham Bennett, CEO of Southern Co-operatives, said: "We have learned that it is best to change as little as possible in the early days."