The deal has not yet been finalized, although it is to be announced within days, said the person, who was not authorized to speak publicly and spoke to The Associated Press on Tuesday on condition of anonymity.
The Los Angeles Times earlier reported the nation's second-largest cable operator will pay around $7 billion to carry the games.
A second person familiar with the situation said that Fox Sports, a division of News Corp., had been prepared to pay more than $6 billion for a 25-year deal to keep the Dodgers on its Prime Ticket regional sports network. But it lost the bidding war after its exclusive bargaining period ended in November. The second person was also not authorized to speak publicly.
The contract marks the second major sports rights deal in three years for Time Warner Cable, which bought the rights to Los Angeles Lakers games in 2011 and launched regional sports networks covering them last year.
After paying an estimated $3 billion for the Lakers rights for 20 years, Time Warner Cable eked out higher fees from other TV distributors in Los Angeles, including DirecTV. The cable operator has said it is bidding for long-term sports carriage agreements to give itself certainty about rising sports costs.
Unlike the Lakers deal, in which Time Warner Cable launched and owns the channels carrying the games, in this case, the team will own a newly launched Dodgers channel but Time Warner Cable will operate it, create the programming and sell the feed to distributors and advertisers. The team will also maintain ownership of the TV rights.
The deal is a coup for the team's new owners, dramatically raising the amount of revenue it was receiving from TV rights, which reached about $40 million a year in 2012.
The new owners include Guggenheim Partners and Magic Johnson. They bought the team out of bankruptcy last year for $2 billion from Frank McCourt and invested another $150 million in a joint venture with McCourt that owns the land around the ballpark.
The new arrangement could test the patience of the nearly 5 million households that pay for TV service in Los Angeles if, as expected, it results in higher monthly TV bills.
After the Dodgers channel launches as planned next year, the area will be home to six regional sports networks, up from two less than a year ago.
Time Warner Cable will have had a hand in launching all four new channels by paying to carry games of the Lakers and Dodgers and helping launch the Pac-12 Networks last year.