Newhailes House, near Musselburgh, dates to the 1680s and is rated as one of the finest Palladian-style country houses in the country.
It was owned by the influential Dalrymple family for almost three centuries before the NTS acquired the estate in 1997.
The first £2.4 million of investment will be divided between £1.48 million to be spent on conservation and landscape enhancement, and £972,000 on commercial and visitor services improvements.
Among the projects is a plan to restore the historic doocot, the installation of a play area for younger children, and the rebuilding of the walled garden.
The estate’s curling pond will be given a synthetic surface to allow usage all-year-round.
“Newhailes is to be one of the first priority projects to be taken forward by the Trust and deservedly so,” said Patrick Duffy, the NTS’ chief operating officer.
“Our ambition is to do nothing less than reawaken Newhailes and return it to the elegance and excitement of its Enlightenment heyday.
“These first steps will provide the means to attract many more visitors to see what was once one of the great cultural and intellectual hotspots – but in ways that are innovative, engaging, accessible and enjoyable.
“In the longer term we aim to secure further funding to create new routes through the estate, re-plant and complete the restoration of the flower garden and ultimately restore, re-present and re-interpret Newhailes House itself.”
The estate, described as “a survivor of old Edinburgh’s rural hinterland”, was purchased by the Dalrymple family in 1709.
The sale was paid for by Sir David, 1st Baronet of Hailes, who served as Scotland’s Solicitor General and Lord Advocate.
Dr Samuel Johnston, is said to have described Newhailes’ library as “the most learned drawing room in Europe”.
The house was a centre of attraction for many figures involved in the Scottish Enlightenment in the late 18th century.