The charity raised £2.2m for the centre including 1,000 pledges of £1,000 as well as contributions from 16 charitable and corporate partners.
Royal Parks chief executive Mark Camley described it as the biggest achievement so far in London's nine royal parks since the foundation's establishment in 1993.
"We are depleted and are concentrating on maintaining the front line rather than the back office," he said. "Education is one of things we have had to draw back from. Fortunately, RPF chief executive Sarah Lom and her team have brought in funding not only for the building but for its ongoing use."
The building features a curved green roof supported by green oak beams, which is said to resemble a tree canopy. One of the two classrooms, which is equipped with microscopes, is named the Trudie Styler & Sting Discovery Room after one bequest. The 2,000sq m surrounding grounds, designed by the Landscape Agency, include a butterfly bank, sensory garden and a large dipping pond complete with underwater endoscope.
A pledge of £800,000 from Tiffany & Co Foundation will fund restoration of the parks' fountains and water features.