In a bold bet on the digital future of entertainment, Time Warner Inc. has named Kevin Tsujihara as chief executive of its Warner Bros. studio — ending a fiercely fought battle for one of the most powerful jobs in Hollywood.

Tsujihara has been president of Warner Bros.’ home entertainment unit, which is responsible for home video, online distribution and video games. In winning the top spot, he edged out rivals overseeing the larger and more prestigious film and television divisions. He will become the first Asian American to run a major Hollywood studio.

When he becomes CEO on March 1, Tsujihara’s priority will be determining how the company can continue to profit from feature films and TV shows as people increasingly watch their entertainment on tablets, game consoles and even smartphones.

Tsujihara, the grandson of Japanese immigrants and the son of a Northern California egg farmer, will become only the fifth leader in the 90-year history of Warner Bros., home of Bugs Bunny, Batman and “The Big Bang Theory.”

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