The school, which was founded by Rosemary Alexander, has trained TV gardeners Joe Swift and Rachel de Thame as well as RHS Chelsea Flower Show designer Philip Nixon.
Alexander said: "We're moving in July because we needed more modern facilities to do what we do. This will give us much more flexibility. But we will be sad to leave Chelsea Physic Garden. I don't think they've quite realised yet (the gap we will leave). It's a mutual decision."
Chelsea Physic Garden general manager Dawn Kemp said new courses would be launched for "lay people" rather than garden designers. "We won't be doing anything like the English Gardening School but we will be looking to develop a new adult education programme," she explained.
Kemp added that an education review two years ago found that the school "should be developing this side of things as an important area to tie in with its charitable status".