Top auto-parts suppliers Delphi Automotive DLPH 1.16 % PLC and Mobileye MBLY -3.60 % NV are joining forces to develop a fully autonomous driving system that car makers could begin placing in their vehicles beginning in 2019. The two hope the development partnership will produce off-the-shelf systems for everything from small cars to sport utilities and pickup trucks--and help them carve out a central role in the race to supply technology for driverless vehicles. The tie-up, which was disclosed on Tuesday, comes as big auto makers and tech companies are moving independently on autonomous-vehicle developments. Delphi, a former General Motors Co. GM -0.38 % spinoff, and Mobileye, of Jerusalem, now supply auto makers with the sensors and software that are the building blocks of autonomous-vehicle development programs. Shares of both have struggled recently as car sales plateau and customers put pieces in place to eventually develop their own gear.