The Lishman family established the store on a pig and poultry farm in 1963. It now has about a million visitors annually with annual sales over £9m.
Founder David Lishman said the sale was an opportunity to ensure the centre's continued success in an increasingly competitive market.
"The business was never put up for sale but after a number of approaches by Wyevale it was decided that the timing was right. There are huge changes taking place within the industry and as a family we have invested significantly in recent years." He added that further investment was required to meet the sector's challenges.
David and Sheila Lishman will retire, while Mick Lishman will remain as head of the nursery.
Wyevale executive chairman Jim Hodkinson said the purchase would strengthen the company's market leadership in the North East because it fitted into its existing coverage in Gosforth, Stockton and Beverley, the former Peter Barratt stores acquired last year.
Wyevale now has 121 outlets across the country after last year's purchase of Blooms' 10 stores for £30m, and the spending of over £50m on Cheshire's Bridgemere Garden World, Sanders' GardenWorld in Somerset, Peter Barratt's three stores, and Old Barn, Sussex.