Dr Williams will take up the appointment in May shortly after he steps down as the Archbishop of Canterbury and takes up a new role as Master of Magdalene College, Cambridge.
He will succeed Dame Anne Owers, who has been chairwoman since 2008.
Dr Williams said he was honoured to be invited to chair the charity's board of trustees.
He said: "I had hoped very much to be able to continue some regular involvement in support and advocacy in the area of international justice and development, and this will allow such an involvement to flourish."