NEW YORK — Time Warner Inc. said yesterday it will formally split off its cable TV business, giving the media conglomerate a $9.25 billion windfall and allowing it to focus on cable network, entertainment and publishing operations.

The separation of Time Warner Cable Inc. gets Time Warner out of the media distribution business altogether, something investors had been clamoring for. The company announced its decision to split up last month and said yesterday that the boards of the two companies had agreed to financial terms.

Time Warner Cable is the second-largest cable provider in the country after Comcast Corp., with about 13.3 million video subscribers. It has been a public company for more than a year, but Time Warner had held on to an 84 percent stake.

Jeff Bewkes, Time Warner's CEO, told analysts in a conference call that Time Warner Cable has grown into more of a "full-fledged telecommunications business" with expansions into high-speed Internet access and digital phone service, and its needs "don't fit as well" with Time Warner's traditional media businesses.

The split-off calls for Time Warner Cable to pay a dividend of $10.27 per share, or $10.9 billion to all shareholders, of which parent company Time Warner will receive $9.25 billion. Time Warner Cable will fund the dividend with its existing credit facility and a $9 billion, two-year bridge loan from a syndicate of banks.

Cable operators tend to have far different capital requirements than other kinds of media companies, with significant investment in infrastructure and new technologies as well as a reliable base of cash flows needed to service the debt to make those investments. Having its own stock will also allow Time Warner Cable to have a currency for potential acquisitions. The deal is expected to close in the fourth quarter.

The split must still receive a favorable tax ruling from the IRS, other regulatory approvals and local franchise clearances.