If the Disney-Fox deal wins governmental approval, as expected, it is not a sure thing that those executives will stay in their roles. Mr. Rice said at the Code Media conference on Tuesday that he didn’t know whether he would remain with the company after the planned merger went through.

Making things even more muddled: Reports on Monday had it that Comcast was revisiting its bid for portions of 21st Century Fox.

Easing Mr. Murphy’s transition to streaming is the fact that he already had a working relationship with Netflix. Fox allowed him to sign a deal with the streaming service in September for a two-season order of a series centered on Nurse Ratched, the villain from the Ken Kesey novel “One Flew Over the Cuckoo’s Nest,” which was made into an Oscar-winning movie. Last week, the streaming company signed up yet another project from Mr. Murphy that may star Barbra Streisand and Gwyneth Paltrow. Both projects come from Fox’s television studio.

The exclusive, five-year deal for the high-profile producer is yet another coup for Netflix. In addition to signing Ms. Rhimes last summer, the company has brought aboard Dave Chappelle, David Letterman, Chris Rock and Adam Sandler with lucrative deals.

Mr. Murphy did not have his hands tied at Fox, which allowed him to push boundaries. And he did not lack for respect: The first season of the FX anthology series “American Crime Story: The People vs. O. J. Simpson,” for which Mr. Murphy served as an executive producer, was a huge hit with critics and won nine Emmys. The Netflix deal, though, will allow him potentially bigger budgets and gives him the latitude to try movies, television or even documentaries.

In his statement on Tuesday evening, Mr. Murphy expressed his gratitude toward Netflix’s chief executive officer, Reed Hastings; its chief content officer, Ted Sarandos; and its vice president for original content, Cindy Holland.

“I am awash in genuine appreciation for Ted Sarandos, Reed Hastings and Cindy Holland at Netflix for believing in me and the future of my company, which will continue to champion women, minorities and L.G.B.T.Q. heroes and heroines,” he said, “and I am honored and grateful to continue my partnership with my friends and peers at Fox on my existing shows.”