Cerberus Capital Management LP struck a $605 million deal to buy 80% of Avon Products Inc.'s North American business and take a nearly 17% stake in the famed cosmetics company.

The Wall Street Journal had reported that the firm was close to a deal with Avon, along with the deal's terms, just after midnight on Thursday.

Avon also said it would suspend its dividend, choosing instead to reinvest cash in its business. It had paid a 6-cent quarterly dividend since late 2012, when it cut the dividend from 23 cents to give it more flexibility.

Shares of the company jumped 21% in premarket trading to $4.94.

The companies said the deal, which has been approved by Avon's board of directors, would help enhance focus on Avon's international markets and rev up its North American business.

"The capital infusion from Cerberus, alongside the suspension of the dividend, and additional operating efficiencies provide us the needed financial flexibility to implement operational and capital plans that fully support the international business," Avon Chief Executive Sherilyn McCoy said in prepared remarks. The CEO said the company would unveil its growth plan in January.

The private-equity firm will pay $170 million for the 80.1% stake in Avon's ailing North American business, which will be split off into a privately held entity.

Cerberus will also make a $435 million preferred-stock investment in the parent, which had a market value of $1.8 billion as of Wednesday's close.

There will be sharp board turnover at Avon as part of the agreement--six directors, including Chairman Douglas Conant, will step down and the board's size will be cut from 12 to 11. Cerberus will take three seats on Avon's board of directors, and the company will name two new independent directors. Cerberus-affiliated Chan Galbato will be named nonexecutive chairman of the board. Avon director W. Don Cornwell will become lead independent director.

The deal comes as Avon is fending off activist investor Barington Capital Group LP, which is part of a group that disclosed a 3% stake in Avon earlier this month and is calling for the company to cut costs and replace its chief executive, Sherilyn McCoy.

It isn't clear how the activists will react to the deal. They have previously indicated they would oppose a deal generally fitting the description of the one struck with Cerberus. A Barington spokesperson wasn't immediately available for comment.

The Wall Street Journal reported in April that Avon was considering strategic alternatives, including a possible sale of the North American business, and in September that Avon was in talks to sell a minority stake to Cerberus or Platinum Equity LLC.

It later reported that Cerberus was closing in on both transactions.

Avon has been beset by difficulties in recent years. Its North American business has been particularly troubled, with sales falling steadily over the past seven years. The business has been more vulnerable to increased online shopping than Avon's operations abroad, in part because some foreign consumers have been slower to embrace the Internet.

World-wide, Avon's revenue declined 19% in the first nine months of 2015 to $5.3 billion, though excluding currency hits it was flat.

Avon got its start in 1886 recruiting women into the workforce as door-to-door sellers of perfume. The company quickly expanded and flourished for generations as American women with more leisure time and money to spend welcomed Avon Ladies into their homes.

Three years ago, Avon turned down an $11 billion offer from rival Coty Inc. and brought in Ms. McCoy to turn the company around. But its results continued to slip as shoppers turned away from the direct sales models and toward the Internet.

Write to Dana Mattioli at dana.mattioli@wsj.com and Nathan Becker at nathan.becker@wsj.com