Southbank Centre chairman Lord Hollick and chief executive Michael Lynch will be stepping down at the end of 2007 and 2008 respectively.
Lord Hollick was appointed to the unpaid role in early 2002.
Months later Michael Lynch was recruited from Sydney Opera House as the centre's chief executive.
The news of their departure is described as a "phased change of leadership".
"I have had the privilege of being chairman of Southbank Centre for six years working with a terrific board of governors and a great executive, brilliantly led by Michael Lynch," says Lord Hollick.
"Together we have achieved a transformation of Southbank Centre with the successful refurbishment of the Royal Festival Hall, and a significant increase in commercial revenue to help to diversify our sources of funding and to finance an increase in our own produced work under the guidance of our strengthened artistic team."
The Labour peer's tenure at the helm of the arts complex has not been without controversy. In 2005 Hollick was memorably described as a "complete prat" by Mayor of London Ken Livingstone during a row about the rent paid by the London Eye for the use of part of Jubilee Gardens.
Vauxhall MP Kate Hoey has also been an outspoken critic of the arts centre's leadership.
Southbank Centre says that an advertisement for a new chairman will be published shortly and the process to appoint a chief executive will commence once the new chairman is in position.
The arts complex changed its trading name from the South Bank Centre to Southbank Centre earlier this year.
• Michael Lynch is due to address the South Bank Forum on Thursday 4 October to update local residents on new proposals for the Hungerford Bridge undercroft, Golden Jubilee Bridge connections and the Festival Riverside extension.