PHILADELPHIA — Shares of Chemours Co. topped $32 for the first time in the company’s history Monday, and the stock of DuPont Co., Chemours’ former owner, also rose after the chemical makers agreed to split the cost of settling about 3,500 lawsuits, and possible future cases, that blame workers and residents’ cancer on DuPont’s former Teflon production at the Washington Works plant on the Ohio River in Parkersburg, W. Va.

“Under the terms of the agreement, DuPont and Chemours will each pay $335.35 million of the $670.70 million global settlement amount” for those cases, plus up to $25 million a year each for the next five years (totaling another $250 million) for possible later claims, Chemours said in a statement.

Lawyers struck the deal five weeks after a federal jury in Columbus, Ohio, told DuPont Co. to pay truck driver Keith Vigneron $10.5 million in punitive damages for his testicular cancer, which Vigneron blamed on pollution from the Parkersburg plant. The jury earlier gave Vigneron $2 million in compensation.

The deal brings “a sound resolution” for the companies and their Ohio Valley neighbors, said David C. Shelton, who is general counsel, corporate secretary and a senior vice president for Chemours. “It settles all indemnification obligations between Chemours and DuPont for all of the approximately 3,500 claims” faced by the companies “and allows us to move forward.”

The lawsuits stem from exposure of workers and neighbors of the plant in Ohio and West Virginia to perflourooctanoic acid (known as PFOA and C8), which DuPont formerly used in making the popular low-friction material Teflon.

“The settlement is not in any way an admission of liability or fault by DuPont or Chemours,” according to Chemours. “Both companies denied any wrongdoing,” DuPont agreed.

The settlement follows decades of Teflon production, followed by more decades of litigation. It “arises from a 2001 class action lawsuit involving DuPont’s contamination of the drinking water supplies” serving 70,000 people in Ohio and West Virginia with PFOA, lawyers for the plaintiffs said in a statement.

Under a 2004 settlement of that lawsuit, DuPont agreed to pay an additional $350 million for local water systems, blood and other health testing, and medical monitoring.

The $670.7 million in the new settlement will address the individual personal-injury claims of the 3,500 or so people who say PFOA in their drinking water led to one or more of six diseases.

“This is a tremendous positive step,” said Rob Bilott, of Taft Stettinius & Hollister LLP, one of the plaintiffs’ lawyers. “We look forward to working with DuPont to finalize this settlement and get these injured class members paid as quickly as possible.”

In a statement, Harold Bock, a spokesman for plaintiffs’ advocacy group Keep Your Promises DuPont, said, “As of this announcement, no checks have been written and no compensation has been paid. Folks who have already had their days in court, (including Vigneron and the cases of plaintiffs Carla Bartlett and David Freeman) have had their awards bogged down in appeals.”

PFOA production began in Parkersburg in the early 1950s. According to testimony, DuPont was aware of PFOA dangers before it acted to protect the public.

What happens, after the initial $670.7 million pays off today’s claims, if more people come forward with cases alleging they were sickened by DuPont?

For the next five years, Chemours pays the first $25 million in new claims, and DuPont pays the next $25 million. After that, Chemours would pay, unless it can show DuPont owes, under terms of the 2014 agreement that separated the two companies.

The “settlement in principle,” as DuPont calls it, is subject to approval by plaintiffs in their cases.