Westwood will resume his quest for a first major on Thursday by teeing off with three-time winner Woods and Ernie Els, who has won the tournament twice.
Woods has struggled with his game since taking nearly five months off following revelations about his private life.
In contrast, Westwood is brimming with confidence after finishing runner-up at the Masters in Augusta in April.
England’s surprise Wentworth winner Simon Khan will play with Americans Brian Gay and Bo Van Pelt.
Khan’s compatriot Ian Poulter, the WGC-Accenture Match Play champion, is grouped with Japan’s Yuta Ikeda and Henrik Stenson of Sweden for the tournament in California.