AT&T Inc. reached an agreement to buy Time Warner Inc. for $85.4 billion in a deal that would transform the phone company into a media giant.

The wireless carrier agreed to pay $107.50 a share, it said in a press release Saturday night. The deal is half cash and half stock.

AT&T Chief Executive Randall Stephenson will head the new company and Time Warner Chief Executive Jeff Bewkes will leave after an interim period following the deal, a person familiar with matter said.

The acquisition will put telecom veteran Mr. Stephenson, 56 years old, atop a business that combines the carrier’s millions of wireless and pay-television subscribers with Time Warner’s deep media lineup including networks such as CNN, TNT, the prized HBO channel and Warner Bros. film and TV studio.

For Time Warner, the deal represents a victory for Mr. Bewkes, 64, who took some heat from investors for rebuffing a takeover bid two years ago from 21st Century Fox at $85 a share. (21st Century Fox and Wall Street Journal-owner News Corp share common ownership.)

Time Warner has agreed to pay a $1.7 billion breakup fee if another company outbids AT&T’s offer, a different person familiar with the plans said. AT&T meanwhile would pay $500 million if the deal gets blocked, this person said.

AT&T will tap $40 billion in bridge loans, a person said, with $25 billion coming from J.P. Morgan Chase & Co. and $25 billion from Bank of America Merrill Lynch.

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