SAN FRANCISCO » Netflix’s Internet video service has landed the U.S. rights to show Disney movies shortly after they leave theaters, a coup that could turn into a costly mistake if the deal doesn’t bring in more customers.

The multiyear licensing agreement announced Tuesday represents a breakthrough for Netflix as it tries to secure more exclusive programming for a popular service that streams video over high-speed Internet connections. The approach is making Netflix more like traditional pay-TV channels such as HBO, Starz and Showtime.

Financial terms weren’t disclosed, but analysts estimate that Netflix will pay Disney more than $350 million annually. That’s a hefty bill that will require Netflix to accelerate its subscriber growth or consider raising its prices — something that management has vowed not to do after rankling customers with rate hikes last year.

Netflix is snatching the rights to the Disney movies from Starz, which had failed to reach terms on renewing a separate licensing agreement with Netflix. Until February, Netflix’s streaming service had access to Disney movies through that Starz deal. The loss had been interpreted as a blow that diminished Netflix’s market value.

Investors applauded Netflix Inc. for trumping Starz to get the Disney rights directly from the Walt Disney Co. — and for winning an exclusive provision that shuts out Starz and other rivals.

Netflix shares surged $10.65, or 14 percent, to close Tuesday at $86.65, its highest closing price since April. That’s still far below its peak of nearly $305, reached around the time that Netflix announced it price increase in July 2011. Rates went up as much as 60 percent for those who wanted to stream Internet video and keep receiving DVDs through the mail, as well.

The stock of Starz’s owner, Liberty Media Corp., sank $5.49, or nearly 5 percent, to $105.56. Disney shares added a penny to $49.30.

It’s the first time that one of Hollywood’s major studios has sold the coveted first-run rights to Netflix Inc. instead of a premium TV network.

DreamWorks Animation SKG Inc. licensed the pay-TV rights to its movies to Netflix last year under a deal that begins in 2013, but those movies don’t wield the same box-office appeal as Disney.

"It’s a bold leap forward for Internet television, and we are incredibly pleased and proud this iconic family brand is teaming with Netflix to make it happen," said Ted Sarandos, Netflix’s chief content officer.

Netflix CEO Reed Hasting is counting on more compelling movies and TV shows to attract more customers. The company is hoping they will become loyal subscribers once they see how much video is available for just $8 per month — a price that undercuts the rates of most pay-TV channels. Furthermore, Netflix is available as a stand-alone service, while premium channels such as Starz require cable or satellite TV packages that average about $80 a month.

Netflix had 25.1 million Internet video subscribers in the U.S. through September, up from 21.5 million at the same time last year. Starz’s premium channel had 20.8 million subscribers at the end of September, up from 19 million a year ago.

Janney Capital Markets analyst Tony Wible said the licensing agreement was a sign of Disney’s long-term faith in Netflix, despite intensifying competition in streaming services from Amazon.com Inc., Comcast Corp. and Verizon Communications Inc.