The GB arm of the grocer, which this week revealed its target for 1100 stores by the end of 2025, said McDonnell will start in his new role on February 1.
He started his career with the business in 2000, joining a graduate programme in Ireland as a trainee buyer.
Most recently McDonnell, 44, was promoted to deputy chief executive for Lidl GB.
Härtnagel returns to his native Germany to lead the business there from March 2022.
The business McDonnell will be in charge of now has more than 880 stores and 26,000 staff across England, Scotland and Wales.
The incoming boss said: “I have worked at Lidl GB now for over six years, during which time we have seen our store estate, colleague and customer numbers grow exponentially. We couldn’t be in a better place as a business and I feel privileged to be taking us forward from here.”