William Randall, who served alongside Frase as co-CEO, will assume the role of chief executive, the company said in a statement.
Randall and Frase were appointed as co-CEOs in May 2016 after the resignation of Yusuf Alireza as chief executive of the Singapore-listed company.
Noble in October said it would sell its Americas-focused oil trading business, headed by Frase, to Vitol for about $580 million, as part of a debt-cutting strategy.
The sale is expected to be complete by the end of December.
Noble has slashed jobs and sold assets to reduce debt and win support from lenders after its share price plunged over the past two years because of questions about its accounting practices. It plans to focus more on coal, liquefied natural gas and freight trading in Asia.
The company reported a third-quarter loss of $1.17 billion last week, hit by charges from disposals of some of its businesses.
Shares of the company plunged 12 percent on Monday to close at their lowest since 1999.
Reporting by Chris Thomas