Johannesburg-based AngloGold will conduct a search for a new chief executive, examining both internal and external candidates.
Mr Cutifani, an Australian, will remain as chief executive of AngloGold Ashanti, a role he has held since early 2008, until March 31.
Chief financial officer Srinivasan Venkatakrishnan and executive vice president business and technical development Tony O’Neill will be joint interim chief executives until a new company head is found.
The company said both executives were well suited for their interim roles, with strong track records at AngloGold Ashanti and in the mining industry.
"Both Venkat and Tony have indicated to the board of directors that they are not at this time intending to put themselves forward for the position of CEO," AngloGold said in a statement.
AngloGold operates the Sunrise Dam mine in WA, where it is also developing the Tropicana mine based on one of Australia's biggest recent gold discoveries.
The company's chairman Tito Mboweni said Mr Cutifani had transformed the business during his five years at the helm.
"Mark led a significant operations and financial turnaround with industry-leading returns, and built a leadership team with outstanding breadth and depth," he said.
The company's safety performance had improved by 70 per cent, the hedge book had been eliminated and the balance sheet rebuilt.
Mr Cutifani said AngloGold Ashanti would prosper in the long-term as the company delivered industry-leading capital returns and developed a project pipeline to deliver long-term sustainable value.
He takes over from Cynthia Carroll at Anglo American, who will leave the company at the end of April. Mr Cutifani’s remuneration package includes an annual basic salary of £1.2 million ($A1.8 million) plus shares and compensation for incentives forfeited at AngloGold.