Hunter, who joined Anglo American in 2009, was formerly director of comms for BP, and prior to that was director of government relations for former PM Tony Blair.
Hunter said: ‘I have had the privilege of working for a great company, with great colleagues, during a period of much change in global mining.
‘I am very proud of the contribution I have made and the team I have assembled to take our work forward.’
Her responsibilities will be assumed by head of government relations Hugh Elliott and head of social performance Jon Samuel, who will both report directly to director of HR and comms Mervyn Walker.
During her time at Anglo American, Hunter built a new government relations and social affairs team.
Chief executive Cynthia Carroll said: ‘Anji has brought considerable experience to her role as group head of government and social affairs. We are very grateful for her work and wish her well for the future.'