Parker will join the company immediately as a non-executive director and will replace Sir Mark Moody-Stuart as chairman on 1 August.
Parker is also chairman of National Grid and joint chairman of the Mondi Group with Cyril Ramaphosa. He also recently stepped down as chair of the Court of the Bank of England.
“Anglo American has many great strengths, including a portfolio of high-quality mining assets, an impressive growth profile, substantial and well advanced efficiency programmes and a unique position in precious commodities,” Parker said.
“I look forward to my new role, leading the board through the next stage of the company’s development.”