Paul Webley, who has led the school since 2006, is receiving treatment for cancer.
In a letter to Soas staff, Professor Webley says he will leave his role as director at some point in the coming year.
“The increasing fragility of my health together with uncertainties about my health in the future have affected my ability to perform as director in the way that I would like,” he writes.
“In the best interests of the school and my family therefore, I have taken the decision to step down from my role as SOAS Director at some point during 2015.”
Professor Webley, an expert on economic psychology, received a CBE in the 2015 New Year Honours list for services to education.
Tim Miller, chairman of Soas’ governing body, said Webley had given the institution “more than eight years of exceptional and inspiring leadership”.
“I have been amazed, but not at all surprised, at his ability to discharge his role as director so effectively and with such energy and professionalism since he first learned of the seriousness of his illness,” he said.
He added that a recruitment process has started to find Professor Webley’s successor, but that the current director “will be an extraordinarily hard act to follow”.