The National Trust was offered the gardens last year but turned down the offer because the gardens failed to "reach the high rung of historic and national importance". Sir Roy threatened to "destroy" the gardens but had a change of heart after Perennial stepped in.
Perennial chief executive Richard Capewell said: "The bequest will come to us on his death - hopefully not for many years. At the moment it is his house and garden and he will carry on running it, so there will be no change to visiting arrangements. When we take over we hope to increase capacity."
Perennial already runs gardens at York Gate in Yorkshire and Fullers Mill in Suffolk. It also had a garden in association with Yardley at the RHS Hampton Court Palace Flower Show this month.