Sir Roy offered the well-known four acre garden to the National Trust last year but the Trust controversially turned it down because the Trust said it failed to "reach the high rung of historic and national importance".
Sir Roy then threatened to "destroy" the garden but has now had a change of heart after Perennial, formerly the Gardeners' Benevolent Fund, stepped in.
After six months of talks, Sir Roy, 79, has now bequested the garden to the charity. The Laskett Gardens is the largest private formal garden to be created in England since 1945.
Charity chief executive Richard Capewell said: "We will look after the garden and use it as an educational public window on the world for us. The bequest will come to us on his death, hopefully not for many years. Then we will take in garden staff and make use of it for uses such as training.
"At the moment it is his house and garden and he will carry on running it, so there will be no immediate change to visiting arrangements. When we take over we hope to increase capacity for visitors – there's lots of potential."
The gardens are currently only open two days a week to groups of more than 20.
Strong has supported Perennial for some years and has hosted Perennial events twice at the garden in the last decade.
Perennial already runs gardens at York Gate in Yorkshire and Fullers Mill in Suffolk and had a garden in association with fragrance brand Yardley at Hampton Court Flower Show this July.
Perennial trustees chair Dougal Phillip said: "Perennial’s history lies in the great gardens of England. The charity was set up by the custodians of gardens of national importance as a pension fund for those who had dedicated their lives to caring for them. Today, in addition to continuing to support all those who work in or have worked in horticulture, Perennial maintains and cares for late 20th century gardens of note. We are delighted to have been offered the opportunity to carry out Sir Roy’s wishes to preserve the integrity of his outstanding garden for future generations."
Strong and his late wife, the designer Julia Trevelyan Oman bought the house and the undeveloped four acre site in Herefordshire in 1973.
Strong said: "It is no secret that the creation of the gardens was a shared passion with my late wife and that they will remain a monument to a marriage. Now that we have opened to the public that passion is shared with the thousands of visitors each year which we welcome. I am heartened that that will continue and also that the gardens will continue to change and develop in the future.
"I see it not only as a bequest to Perennial but also to the county of Herefordshire. I am thrilled, as I reach my 80th birthday, that a plan for The Laskett’s future has been secured. I have supported the work of Perennial for many years and see this new partnership as a wonderful extension of my continued love of gardens and those who dedicate their time to serve them."
The garden will be left to Perennial with a "generous" endowment to ensure its maintenance for years to come.