Yesterday (Tuesday 8 March) Livingstone reneged on his original decision to recommend refusal of the proposals by Barnes-based Barnsley Hewett & Mallinson.
Livingstone said: 'This decision will allow the Royal Ballet School to extend the valuable contribution it makes to the communities throughout London and beyond, and reach out to many Londoners who have not previously had access to classical dance.'
The mayor initially believed that the school's plans to extend and refurbish its Lower School at White Lodge in Richmond Park had contravened elements of the London Plan regarding development on Metropolitan Open Land.
But after rethinking its ideas the school has now put forward a package of new planning obligations for a comprehensive outreach programme.
This will include Greater London and will meet the objectives of the London Plan about which Livingstone originally expressed concern.
Chairman of the Royal Ballet School David Norman said: 'The school is delighted that the mayor has now decided to allow the planning application to go forward.
'We have agreed with the mayor to expand national outreach work to further include London schools. This will mean that children from diverse cultural and economic backgrounds will learn about classical dance,' he added.