AT&T Inc. reached an agreement with an activist investor that had been pressuring the telecom giant to revamp its strategy, and said its chief executive would stay at the helm through next year.

Chairman and CEO Randall Stephenson has used big acquisitions of Time Warner and DirecTV to turn AT&T into a major media provider, a shift that activist Elliott Management Corp. had called into question. Mr. Stephenson said Monday that AT&T would forgo big takeovers in the coming years to focus on improving the bottom line.

“I...