Young plants manager Paul Hansord said: "There will be no Thompson & Morgan branding on the business whatsoever.
"It (Vernon) has a good database that we can utilise better than has been the case so far. There is real interest in geraniums at the moment. They are a popular crop and we can build on that."
The Surrey-based grower was started by Jack Cox and continued by his daughter and son-in-law, Janet and Derek as well as Jack's granddaughter, Liz.
Meanwhile, Whitehall Garden Centre has bought the Highfield Nurseries mail-order business and website to develop sales of plants via the internet.
Highfield started as a mail-order nursery in Gloucestershire. It now has a garden centre nearby that has become the main part of the business.
Highfield director Tim Greenway explained that when mail-order despatch director Trevor Wellington retired, it sold that "small part of the business" to Whitehall.
"The mail-order business never kept up with internet development because it always had a very strong catalogue, so we probably lost out," Greenway added. Highfield has a garden centre in Gloucester and a nursery that grows for it.