By Angela Chen 

Charter Communications Inc. agreed to buy cable operator Bright House Networks LLC for $10.4 billion in cash and stock, the latest deal in a rapidly consolidating pay-television industry.

Bright House is the sixth-largest cable operator in the U.S. and serves approximately 2 million video customers in central Florida, as well as Alabama, Indiana, Michigan and California.

Charter, currently the country's fourth-largest cable operator, said it would become the second-largest cable operator after the deal. Shares of Charter jumped 6.9% to $196 in premarket trading.

"Bright House Networks provides Charter with important operating, financial and tax benefits, as well as strategic flexibility," Charter Chief Executive Tom Rutledge said in a news release.

Connecticut-based Charter has struggled as consumers have turned away from more-traditional forms of pay television toward Internet-based entertainment services such as Netflix and Amazon Prime. It had earlier sought to purchase Time Warner Cable, which had a long-standing arrangement to handle programming and technology acquisitions for Bright House.

The merged business announced Tuesday would be conducted through a partnership that Charter will own 73.7% and Advance/Newhouse--the parent company of Bright House Networks--will own the rest.

The Bright House cable systems are part of the Newhouse family's media empire, which also includes publisher Advance Publications Inc. as well as an interest in Discovery Communications Inc.

In addition, Liberty Broadband Corp. has agreed to purchase $700 million of shares in the new company after the deal closes, with equity ownership totaling about 19.4% of the shares outstanding, out of the 26.3% owned by Advance/Newhouse.

Advance/Newhouse has agreed to grant Liberty Broadband a voting proxy on its shares, capped at 6%, for the five years following the close of the transaction, such that Liberty Broadband would have total voting power of about 25% at closing.

The Charter and Bright House deal comes amid changes in how viewers consume television.

For years, TV channel owners and their pay-TV distributors--cable and satellite providers--were able to count on two reliable trends: that pay-TV subscriptions in America would grow each year, and that consumers would submit to paying ever-higher cable bills. In the past two decades, the pay-TV industry has grown by about 40 million subscribers to a total of about 100 million homes, and typical cable bills increased at a compound average annual growth rate of about 6.1%, according to the Federal Communications Commission.

But evidence mounted over the past couple of years that something fundamental was changing. In 2013, the industry's base of subscribers contracted for the first time. Last year, pay-TV subscriptions fell by 129,000 industrywide, according to MoffettNathanson, even as analysts said new household formation surged, typically a good sign for the industry in years past.

Instead, consumers increasingly are cutting the cable cord and signing up for TV services delivered over the Internet. Others, meanwhile, are "shaving" it and downgrading to cheaper packages that operators began to offer.

In response, pay-TV distributors have begun to merge. Comcast Corp. has announced a deal for Time Warner Cable Inc., and AT&T Inc. is planning to buy DirecTV. The deals, though, have been held up as regulators study the implications of such moves.

As part of Comcast's $45 billion agreement to buy Time Warner, Charter agreed to pay about $7.3 billion in cash for 1.4 million existing Time Warner Cable Inc. customers, while it will swap another 1.6 million customers with Comcast.

Write to Angela Chen at angela.chen@dowjones.com

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