"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," Thompson said, as quoted in the Wednesday release.
McDonald's did not explain why Thompson, who has been with the company for over 20 year, is leaving.
The burger chain has been losing customers in the United States because of its complicating menu and people's increased preference for other fast food chains, such as Chipotle Mexican Grill.
Last week, McDonald's reported on its profits, announcing that it has seen a steady decline in same-store sales in the United States and warning that business would be weak in the first half of 2015.
McDonald's, which is one of the biggest fast food restaurant chains in the world, has 451 restaurants in Russia, where concerns are growing for the safety of McDonald's products.
Since August Russian consumer protection officials have carried out over 200 safety inspections at various McDonald's premises throughout the country.
According Russian public health watchdog Rospotrebnadzor numerous breaches of sanitary regulations, including some of the products testing positive for E-coli bacteria, have been found at the burger chain's restaurants.