The centre is being designed by architect Andrew Yeats from EcoArc, a practice specialising in sustainable design. It will feature a teaching garden, three classrooms and a library and exhibition space, which will be open to all garden visitors.
The building will be supplied with renewable energy, using wind turbines and solar panels. The development will have super-insulated walls and a sedum roof. Rainwater will be harvested and a natural reed bed sewage system will be incorporated into the landscaped gardens.
Landscaping around the building has been designed by Tom Stuart Smith, and the Landscape Agency is drawing up a detailed design.
RHS director of gardens and estates Jill Cherry said: "Everything we teach in the learning centre will incorporate themes of sustainability and good environmental practice, so children will become more in touch with the world around them."
More than 10,000 schoolchildren a year will be able to use the learning centre, three times the number with which the garden can currently cope.
The RHS also plans to use it as a base for outreach programmes, as it aims to engage with "hard-to-reach" communities and schools in and around Yorkshire. Construction will begin in January.