TOKYO—Sony Corp. said Tuesday that it will move the headquarters of its PlayStation videogame unit to California, a move that reflects the industry’s view of the U.S. as offering the greatest growth potential.

As part of the move, Tokyo-based Sony Computer Entertainment, the videogame unit, will merge with San Mateo, Calif.-based Sony Network Entertainment International LLC, which provides PlayStation’s network services. The change will take effect in April, and the new company will be called Sony Interactive Entertainment...