Meredith said they will have no influence in the combined company.
Meredith had expressed interest in buying Time earlier this year and then walked away because it could not secure the necessary financing.
In May of this year, Time Inc announced plans to sell some magazines or other properties as it tried to push ahead with a digital strategy.
Rothschild & Co.'s renewed push in the U.S.is getting a boost from the Koch brothers.
Meredith's deal is backed by $650 million from Koch Equity Development, the investment arm of Koch Industries, an industrial conglomerate rooted in the oil and gas business.
Meredith's offer is for $18.50 per Time share, up about 10% from the shares' closing price of $16.90 Friday.
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The Koch brothers have spent decades building a network of wealthy political donors who pledge money to conservative causes and their advocacy groups.
Meredith's brands include Better Homes & Gardens, Allrecipes, Parents and Shape. The publishing giant has a portfolio of 17 television stations in 12 markets, which reach an estimated 11% of USA households TVs.
Meredith also anticipates savings of $400 million to $500 million in the first full two years of operation thanks to synergies.
Once the two companies are merged, Meredith says they will serve almost 200 million consumers, with its digital media business reaching 170 million monthly unique visitors in the U.S. Meredith and Time Inc. made combined revenues of $4.8 billion in 2016, including $2.7 billion in total advertising revenue (with $700 million of that from digital advertising) and adjusted EBITDA of $800 million. It is unclear how much influence the Kochs would have on Time, which includes Time magazine, People, Sports Illustrated and Entertainment Weekly among its stable of publications.