A collection of small seedlings and buds from the 50ft (15m) tree were propagated by the National Trust at the charity’s conservation centre in Devon.
King Charles is patron of the charity, which has so far bred more than 100 seedlings and more than 40 cuttings.
The first seedling will be looked after by horticulturalists until it is ready for planting.
“It is wonderful news that His Majesty will one day have the very first sapling grown from this iconic tree,” said Hilary McGrady, director general of the National Trust.
“The new tree will be seen by many thousands each year and will be the first of many Sycamore Gap saplings planted at different places, in Northumberland and beyond.”
She added: “These new green shoots are keeping the story of the Sycamore Gap alive and are serving as a reminder of the simple and much-needed hope, joy and respite that nature can bring.”
The seedling was first seen by the public at the Chelsea Flower Show on 20 May, when Dame Judi Dench placed it in the Octavia Hill garden.
The National Trust gifted the King the seedling on 27 May, which is Celebration Day, a national day dedicated to remembering and celebrating people who are no longer with us.
