Skinner has worked at McDonald's for 41 years. Thompson will take over the role from July 1 this year.
Thompson is 48 and has previously held a number of executive roles at the burger chain. He became chief operating officer in January 2012.
His previous roles include president of McDonald's US from 2006 until 2010, a role in which he was responsible for the strategic direction of the US business.
The change does not impact on the role of Jill McDonald, UK chief executive of McDonalds.
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