The former CEO of McDonald's who was fired a few days ago has resigned from the board of Walmart, according to a company filing.

Stephen J. Easterbrook was sacked after he had a relationship with an employee. The U.S. fast-food giant said the relationship was consensual, but Easterbrook had "violated company policy" and shown "poor judgement".

In a regulatory filing on Monday, Walmart said: "On November 4, 2019, Stephen J. Easterbrook informed Walmart Inc. that he will resign as a member of the Board of Directors of the Company, effective immediately.

"Mr. Easterbrook’s decision to resign was not due to any disagreement with the Company on any matter relating to its operations, policies or practices."

Easterbrook had joined the Walmart board in 2018. He sat on the Compensation and Management Development and Strategic Planning and Finance committees, according to the company website.

The British businessman reportedly earned nearly US$16m last year from his role at McDonald's, which he had held since 2015.

Bloomberg estimated that he will leave with more than US$37m, the bulk of which includes previously granted shares. In exchange, Easterbrook has agreed not to work for a competitor for at least two years.

Chris Kempczinski, most recently president of McDonald’s USA, as CEO and president, effective immediately. 

Meanwhile, in October Walmart US announced John Furner will take over as CEO. He will take over from Greg Foran, who is moving onto a role at Air New Zealand.