Chris Valasek and Charlie Miller made names for themselves a couple of years ago when they remotely hacked into a Jeep made by Fiat Chrysler Automobiles NV. Now they are going to work for General Motors Co.

GM’s self-driving-vehicle subsidiary, Cruise Automation, has hired the cybersecurity experts from two major ride-sharing firms, the latest salvo in a war for tech talent between Silicon Valley and Detroit. Mr. Valasek was working as Uber Technologies Inc.’s top cybersecurity expert, and Mr. Miller had worked at Uber before leaving in March to join Didi Chuxing, China’s largest ride-hailing firm.