This week Thompson announced a 4% fall in US sales and 7% decline in global sales, while the UK generated "positive comparable sales and operating income". He has been in the top job for two-and-a-half years and will be replaced by Easterbrook in March.
Easterbrook was elected to McDonald’s board of directors and becomes the fast-food chain's first-ever non-US chief executive officer.
He was senior vice-president and chief brand officer of McDonald’s and has been credited with leading the brand’s marketing, menu innovation and for creating "an infrastructure for its digital initiatives".
He has also been lauded for turning around McDonald’s UK business, which he ran from 2006, before becoming president of McDonald’s Europe.
He left the group in 2011 to run Pizza Express, and a year after that joined Wagamama, before returning to McDonald’s in 2013 to head up its global brand operations.
His appointment comes at a challenging time for McDonald's. Earlier this week, it reported that full-year profit down 15% to $4.7bn and global sales down 7% to $6.5bn. The results fell short of analyst predictions, which forecast sales of $6.7bn.
Thompson, who joined McDonald’s in 1990 as an electrical engineer, said in a press release: "It’s tough to say goodbye to the McFamily, but there is a time and season for everything.
"I am truly confident as I pass the reins over to Steve, that he will continue to move our business and brand forward."
Easterbrook said: "I am honoured to lead this great brand, and am committed to working with our franchisees, suppliers and employees to drive forward our strategic business priorities to better serve our customers."