Mr Snowman has been appointed by Glyndebourne's owner, Sir George Christie, to be in charge of artistic policy at the Sussex opera house from September.
The South Bank Centre recently failed in its application for pounds 75m of lottery money for an ambitious scheme by the architect Richard Rogers to improve the Royal Festival Hall and cover the Queen Elizabeth Hall, Purcell Room and Hayward Gallery with a glass roof.
Mr Snowman was deeply disappointed when the scheme was turned down by the Arts Council, and his departure comes as little surprise. Possible successors include Patrick Deuchar, former chief executive of the Royal Albert Hall, and in a straight swap the recently departed general director of Glyndebourne, Anthony Whitworth Jones.
Elliott Bernerd, chairman- elect of the South Bank Centre, said last night: "I know how disappointed Nicholas has been over the considerable delays that have affected our redevelopment plans, and his personal contribution to the Rogers project has been particularly appreciated by the board ... We are seeking a successor to Nicholas who will combine strong entrepreneurial skills with a commitment to the artistic activities of the centre."
Mr Snowman said yesterday: "I have achieved my artistic ambitions at the South Bank Centre. And I am still confident there will be a redevelopment of the centre. The Glyndebourne job is a dream come true. Opera has always been central to my life."