McMahon replaces Steve Nelson, who is retiring from UnitedHealthcare.
The nation's largest health insurer also said Daniel J. Schumacher, currently president and chief operating officer of UnitedHealthcare, was named president and chief operating officer of Optum, the company's health-services arm.
"At a time when UnitedHealth Group is performing strongly in the marketplace on multiple dimensions, we are advancing leaders who will improve the overall health and well-being of the people we serve and their communities, and further enhance the performance of the health system," said David S. Wichmann, CEO of UnitedHealth Group. "Our consistent approach over the years is to provide our executives with a breadth of experience across the company, ensuring they can deploy the full set of our capabilities to everyone we serve in the interest of achieving better health outcomes and a better experience for people while meaningfully lowering health care costs."
In his new role, Schumacher will be in charge of OptumInsight, the company's data, analytics and technology business, Optum Technology and Optum operations, UnitedHealth Group said in a statement.
The stock rose slightly in premarket trading to $246.50. Shares have fallen about 1.1% so far in 2019.