WASHINGTON (Reuters) - A majority of the five-member U.S. Federal Communications Commission has voted to approve Charter Communications Inc's (CHTR.O) acquisitions of Time Warner Cable Inc TWC.N and Bright House Networks, two sources briefed on the matter said on Thursday.

The deals, which would create the second-largest U.S. broadband provider and third-largest video provider, won the backing of FCC Commissioners Jessica Rosenworcel and Michael O'Rielly this week, the sources said on condition of anonymity.

FCC Chairman Tom Wheeler had already voted to approve them.

The two other FCC commissioners have yet to vote on the matter.

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O'Rielly dissented in part, meaning the final conditions of the agency's approval could change before the full vote is completed and made public. The U.S. Justice Department gave antitrust approval to the acquisitions with conditions on April 25.

The FCC declined to comment on Thursday.

Charter and Time Warner Cable shareholders have approved the companies' deal. Privately-held Bright House also is in favor of its acquisition.

The only other outstanding approval needed is from California. A state administrative judge last month recommended that California's public utilities commission approve the deal. The decision could come as early as May 12.

The Justice Department's approval carried conditions designed to protect competition, coming at a time when the pay television industry faces stagnation due to new competition from over-the-web rivals like Netflix and Hulu.

The Justice Department said Charter agreed to refrain from telling its content providers that they cannot also sell shows online as part of the approval process.

The FCC's Wheeler said last month that approving the deals "will directly benefit consumers by bringing and protecting competition to the video marketplace and increasing broadband deployment."

The conditions placed on FCC approval would require Charter to extend high-speed internet access to another two million customers within five years - with one million served by a broadband competitor, Wheeler said.

Charter has valued its deal for Time Warner Cable at $56.7 billion, excluding debt, and the acquisition of Bright House at $10.4 billion.

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Charter, backed by billionaire John Malone's Liberty Media Corp LMCA.O, had pursued Time Warner Cable as far back as 2013.

The two companies had acrimonious exchanges in 2013 and early 2014 that ended with Time Warner Cable rejecting unsolicited approaches by Charter and instead finding a white knight in Comcast Corp (CMCSA.O), the No. 1 U.S. cable services provider.

(Reporting by David Shepardson; Editing by Chizu Nomiyama)