Chevron Corp. has agreed to buy Anadarko Petroleum Corp. in a $33 billion deal that expands its shale-drilling ambitions and places it just behind Exxon Mobil Corp. as one of the world’s largest publicly traded producers of oil and gas.

The combined company is set to become the leading operator in the heart of America’s fracking boom in West Texas and New Mexico at a time when the U.S. pumps more crude than Saudi Arabia and Russia. The value of Chevron and Anadarko’s U.S. drilling prospects exceeds $100 billion, more than...