Dr Byron Grote will continue as audit committee chair, as well as take on Hampton's role as senior independent director from January 1, 2019 onwards.
He has over 35 years' experience in the natural resources sector.
Anne Stevens will take Hampton's place as chair of the remuneration committee at the start of 2019, while Ian Ashby will take on Thompson's position as chair of the sustainability committee on April 30, 2019.
Anglo chairman Stuart Chambers said Stevens' global executive and board experience and Ashby's extensive mining career would "further enhance our committee deliberations under their leadership".
Both Hampton and Thompson had reached nine years on the Anglo board, the point at which directors are no longer seen as independent.