Tribune said Zell plans to invest $315 million in the deal and the company will sell the Chicago Cubs baseball team at the end of this season.
He will eventually become chairman of the Chicago-based company's board when the deal is complete sometime in the fourth quarter.
Tribune said the buyout will be conducted as a two-part deal. The first stage, expected to be completed in the second quarter, will involve a cash tender offer of $34 per share for 126 million shares. That offer will be paid for with a $250 million investment from Zell, the company said.
The remaining shares will be purchased for $34 per share in the second phase.
Tribune has about 240 million shares outstanding, according to a regulatory filing.
Tribune, which owns the Chicago Tribune, Los Angeles Times, The (Baltimore) Sun, TV stations and the Chicago Cubs, had been considering a competing offer from Los Angeles billionaires Eli Broad and Ron Burkle.
The company's board reportedly spent much of the weekend sifting through the two competing offers.