Google is moving onto Uber Technologies Inc.’s turf with a ride-sharing service to help San Francisco commuters join carpools, a person familiar with the matter said, jumping into a booming but fiercely competitive market.

Google, a unit of Alphabet Inc., began a pilot program around its California headquarters in May that enables several thousand area workers at specific firms to use the Waze app to connect with fellow commuters. It plans to open the program to all San Francisco-area Waze users this fall, the person said....