The design by Arabella Lennox-Boyd wraps around a 19th-century gunpowder store, which has been transformed into a £14.5 million extension for the gallery in Hyde Park.
The grade II* listed neoclassical Magazine building from 1805 was extended by the late Pritzker Prize winning architect Zaha Hadid. The project was announced nearly three years ago.
Lennox-Boyd said the rear of the space was defined by a woodland garden with planting such as helliobores overlooked by a border with herbaceous plants and grasses.
Waves of box and trees marked the front of the garden, with a careful selection of trees relating to the edge of the park. The idea was to blend garden and park rather than separated them, she said.
"The garden ebbs and flows much like Zaha Hadid's built forms, which are sensual and curvy. I try never to impose my design on buildings," explained Lennox-Boyd.
"Zaha's recent death was awful; it's really really sad she won't be here for the opening. We talked a lot about plants and I was determined not to desecrate her wonderful building."
Last week the gallery said Lennox-Boyd's creation would be officially opened on 18 May. Until recently the building stored flag poles.
Royal Parks invited tenders for its use four years ago, with the Serpentine beating hopefuls including Damien Hirst who wanted to use it to show his art.