The plans for the 3.65 hectare Astroturf tennis court have been approved by the Borough Council of King's Lynn and West Norfolk.
It will replace an existing tennis court that has fallen into disrepair. The new court will be built 20 metres away to improve views from Anmer Hall and the old court will be turned into part of the garden.
The plans involve the removal of 10 trees, including a silver birch, Japanese and Norwegian maples, a fruit tree and a laburnum.
The laburnum, which was previously identified as a Japanese maple in the architect’s plans for the court, was identified in a tree survey. News reports said that the royal couple have been warned of the danger the poisonous tree can pose for children and animals.
The tree survey report, by M. J. Tree Services, said the trees are of "low and moderate amenity value" and concluded their removal would have "no significant impact" on the landscape.
Also, the proposals include the planting of three new common oak trees on the site of the old tennis court and a hedge row to screen the development for park land.