The work is expected to attract some controversy as the RFH will close for 18 months during its refit, starting in July - a move likely to result in redundancies.
The South Bank Board operates the area between County Hall and Waterloo Bridge, including RFH, which was built in 1951 for the Festival of Britain.
The trust also manages the Queen Elizabeth Hall, Purcell Room and the Hayward Gallery.
More than 60 per cent of the board's funding comes from the Arts Council for England, with the rest from box-office sales and donations. The board oversees 900 events a year, which attract around three million visitors.
Fishburn Hedges' PA brief is unaffected. Board head of press Sue Rose declined to confirm any details.