General Motors Co. plans to become the first company to test self-driving cars in New York City, a move aimed at asserting leadership in the race to develop autonomous cars and a potentially important step toward commercializing the technology.

GM will deploy a fleet of self-driving Chevrolet Bolt electric cars early next year in a 5-square-mile section of lower Manhattan that engineers are mapping, said Kyle Vogt, chief executive of Cruise Automation, the driverless-car developer GM acquired last year. The move could be...