Netflix Inc. cut a deal to debut a new television series by Oscar-nominated director David Fincher on its Internet streaming service, in an agreement that departs dramatically from how traditional television programming is made and aired.

Under the deal with independent studio Media Rights Capital, Netflix said "House of Cards"—a political drama to be executive produced by Mr. Fincher and star Kevin Spacey—will begin playing exclusively on Netflix's Internet streaming service late next year.

Netflix...