General Motors Co. has struck a deal with a Detroit-based hospital system to offer a new coverage option to employees, upending the traditional benefits setup in an attempt to lower costs and improve care.

The auto maker’s agreement with Henry Ford Health System covers everything from doctor visits to surgical procedures. By signing a contract directly with one health-care provider, as other companies have done, GM says it can offer a plan that costs employees less than other options while also promising special customer-service...