Chevron Corp. CVX 0.55% Chief Executive John Watson is planning to step down as the energy giant seeks new leadership for a changing oil world, according to people familiar with the matter. The transition is expected to be announced next month, although Mr. Watson’s successor hasn’t yet been finalized by the board and plans could change, the people said. Mr. Watson isn’t expected to depart immediately and is likely to remain after the announcement for an orderly transition, the people said. His likely departure underscores the dramatic shift under way at big oil companies as they adapt to a prolonged period of lower prices brought about by the U.S. shale boom. While the companies once favored swashbuckling leaders who bet billions on megamergers and pricey projects in far-flung regions, many are now turning to executives adept at squeezing every last dollar from a barrel through refining, and shorter-term investments that turn a profit faster.