Amazon just made a major commitment to what the company sees as its great new hope: Phoebe Waller-Bridge.

The streaming service signed a development deal reportedly worth $20 million a year with the British writer, actor and producer of the sleeper hit series “Fleabag.”

“Jennifer’s been looking for Amazon’s ‘Game of Thrones’ — something big, British, a bit shocking, sexy,” said an Amazon executive of the company’s studio chief, Jennifer Salke. “She found it in Phoebe.”

Waller-Bridge rocketed from cult favorite to the new queen of comedy last month when she bagged three Emmys — for best comedy actress, best comedy series and writing — against all odds: The 34-year-old was up against two of Hollywood’s darlings, “Veep” and “The Marvelous Mrs. Maisel.”

“She and ‘Fleabag’ are much loved at home, but I never thought she’d break out in the US like this. Neither did she,” said a British producer in the know.

Another Amazon insider recalled how, when the star and her boyfriend walked into the company’s post-Emmys party late, “Everyone burst into applause. That doesn’t happen in this town. In that moment, she and [playwright and movie director ] Martin McDonagh became a power couple. Everyone from Netflix to the big studios is chasing both of them.”

Waller-Bridge has become enough of a household name that she’s hosting “Saturday Night Live” this weekend, with musical guest Taylor Swift.

While it might seem that she came out of nowhere — “Fleabag” had just two six-episode seasons on Amazon — the actress also developed the buzzy series “Killing Eve,” which airs in the US on AMC. And she’s Daniel Craig’s handpicked writer for “No Time to Die,” the next Bond film, due in April 2020.

An MGM executive who has visited the London set of “No Time To Die” told The Post: “The studio and filmmakers love Phoebe’s voice. They’re already talking to her about the next Bond, whether Daniel’s in it or not. If he does one more, it would be because of her.”

Waller-Bridge has said that her role on “Fleabag” — a mixed-up young woman with booze, sex and family issues — is a bit of an alter-ego. As with the character, she lost a female friend to suicide.

She grew up in privilege, the daughter of a wealthy financier and the granddaughter of a baronet, attended an all-girls Catholic school (hence “Hot Priest”) and graduated from the Royal Academy of Dramatic Arts. Her older sister composes the music for “Fleabag.”

After starting out on stage, she nabbed small parts in the films “Albert Nobbs” and “The Iron Lady” and the TV series “Broadchurch.” Her first splash in the UK came with the Channel 4 sitcom “Crashing,” about slacker millennials, in which she starred and helped create. But it was when she created the one-woman play “Fleabag,” which ran at London’s Soho Theater for two sold-out weeks in 2013, that her career really began to take off. (Waller-Bridge revived the stage show for Broadway earlier this year.)

She was married to Conor Woodman, 45, an Irish writer, from 2014 to 2017. “They were well-matched,” says a British casting director who knows both of them. “I just think she wasn’t ready to play ‘the wife.’ ”

Shortly after her divorce, Waller-Bridge was spotted with McDonagh at a screening of the film “Three Billboards Outside Ebbing, Missouri,” which he directed. The two reportedly share her home in the Kensal Rise area of northwest London.

Before her Amazon deal kicks in, Waller-Bridge is executive-producing the HBO comedy series “Run,” starring Domhnall Gleeson, and it’s said she’ll appear in a recurring role.

And while Amazon went all-in on her future based in large part on “Fleabag,” Waller-Bridge is in no hurry to make a third season of that series. As she told Seth Meyers last week on “Late Night,” she might ­revisit it — when she’s 50.

Still, Amazon boss Salke isn’t giving up on her investment. Asked last week at a Hollywood forum if she thinks there might yet be ­another season of what’s currently the buzziest show around, she said: “I’m a believer.”