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Cockerill will take over the role in June, after nine years as a senior executive and six years as CEO at Gold Fields Limited.
The new CEO said he recognised the importance of the world-wide issues surrounding energy, and looked forward to taking on a global role in a company that has "tremendous depth of experience" in the resource and energy sector.
Anglo American also announced the appointment of Kuseni Dlamini as head of Anglo American South Africa, with day-to-day responsibilities, including internal transformation of the South African business and alignment with the group's global strategy.
Dlamini comes to Anglo American from his role as executive chairman of the Richards Bay Coal Terminal, in which Anglo American is a 27% stakeholder.
In a third senior executive appointment, Russell King has been appointed chief strategy officer with the role of working closely with executive management to define and execute the group strategy and lead performance monitoring processes.
King has been with Anglo American since 2001, and previously acted as head of human relations, business development and sustainable development.