The chief executive of the streaming service Hulu, Mike Hopkins, is leaving to become chairman of Sony Pictures Television, Hulu said on Tuesday. Randy Freer, a member of the Hulu board, will succeed him.

Mr. Hopkins, who has been Hulu’s chief executive for the past four years, will be moving into the role at Sony that Steve Mosko vacated more than a year ago. Mr. Freer, the Fox Networks Group’s chief operating officer and previously a co-president at Fox Sports, will take over the Hulu job on Monday.

Hulu got a big boost last month when its “The Handmaid’s Tale” became the first show from a streaming service to win the Emmy Award for best drama.

The change at the top also comes as Hulu’s parent companies — including Comcast, Disney, Time Warner and 21st Century Fox — are making a more concerted effort to sell Hulu the back libraries of their shows, rather than making similar deals with Netflix.

Still, the service’s performance remains a bit of a mystery. It last disclosed its total number of subscribers 17 months ago; at the time, the figure stood at 12 million. It is unclear whether subscriber growth has slowed, or how well its live television service is faring. By comparison, Netflix announced last week that it now has 51 million paying subscribers in the United States.

Hulu is in better shape than one of its other rivals, Amazon, which has undergone tumultuous leadership changes in the past week. First, Roy Price, the chief of Amazon Studios, resigned last week after being accused of sexual harassment. Joe Lewis, Mr. Price’s main lieutenant, left this week. And Tuesday, Amazon confirmed that Conrad Riggs, the leader of its unscripted programming, was also departing.

At Sony Pictures Entertainment, Tony Vinciquerra, the chief executive, has focused primarily on the studio’s television division since joining the company in May. A month he came aboard, Sony’s top two television programming executives, Jamie Erlicht and Zack Van Amburg, left for Apple, which is finally taking the plunge into expensive, original programming. After their departure, Mr. Vinciquerra promoted three executives.

Television production — all but abandoned by Sony 16 years ago — has emerged as a financial engine for the company because of the increasing appeal of streaming services. With shows like “The Crown,” “Better Call Saul” and “The Goldbergs” in its stable, Sony Pictures Television contributed more than 90 percent of the entertainment company’s total income last year. Sony also operates an array of fast-growing overseas cable networks.

Sony Pictures Television will make more than 30 series for the 2017-18 season, including chestnuts like “Jeopardy” and “The Young and the Restless.” New series include “The Good Doctor,” which has been a hit for ABC.

Sony’s movie unit, long an industry laggard, has recently shown signs of a turnaround. “Spider-Man: Homecoming” took in $880 million worldwide over the summer. Sony was even able to turn the disastrously reviewed “The Emoji Movie” into a hit, with global ticket sales of $208 million. There have also been flops — including “The Dark Tower” and “Rough Night” — but box office analysts say Sony has a potential holiday juggernaut in “Jumanji: Welcome to the Jungle,” which is set to be released on Dec. 20.