The Group will run the retail outlets from Tuesday, April 3.
Garden Centre Group chief executive Nicholas Marshall said:
"We are delighted to have taken on the plant centre and gift shop at Westonbirt. We are working closely with the Forestry Commission to ensure a smooth handover.
"We shall be offering a superb and expanded range of plants and gardening products. We shall be stocking top quality British grown plants, rare and unusual varieties, specimen trees, shrubs, conifers, acers and our David Austin range of roses.
"Our gift shop will showcase a range of products, many of which are from British designers and manufacturers such as Emma Bridgewater and Garden Trading."
The Garden Centre Group now has 128 garden centres nationwide.
Simon Toomer, arboretum director, added: "We chose The Garden Centre Group because it brings with it a wealth of experience and knowledge from working with similar organisations.
"We believe it will bring fresh ideas to retail at Westonbirt Arboretum."
Westonbirt Arboretum is managed by the Forestry Commission.