The trust aims to make Dyffryn Gardens and Dyffryn House, which will open to visitors for the first time this year, "one of the most significant visitor attractions in south Wales".
Trust representative Ken Smith said the gardens would develop "organically" with no immediate projects planned. He added that the trust hopes to increase visitor numbers from 30,000 to 100,000 in the long term.
The grade II listed house and its grade I listed garden were created by Welsh coal baron John Cory and his family after he bought the site in the late 19th century.
With the help of landscape architect Thomas Mawson, the Cory family developed a 22ha garden. The estate passed to the council in 1996 and has undergone extensive restoration with £6m from the Heritage Lottery Fund.