Pechiney's board accepted a cash-and-stock bid of 48.5 euros per share, which valued the French company just over 4.0 billion euros (4.5 billion dollars), it said.
"The new offer is a cash/share offer up to 48.5 euros consisting of 47.5 euros per share plus a one euro per share supplement if the tender results reach at least 95 percent," a company statement said.
A July offer of 41 euros per share was rejected by Pechiney directors who described the offer as "ridiculously low". They also turned away an improved bid in late August, saying it "continues to fall short of Pechiney's true strategic value".
But Alcan's final offer was close to that of its second bid.
On Friday, the Pechiney statement said: "The board of directors is pleased that this combination would allow Pechiney's employees to contribute to a global leader in aluminum and packaging activities.
'Best interest of the company'
"It has consequently determined to recommend to Pechiney shareholders to accept Alcan's new offer, which it views as being in the best interest of the company's shareholders, employees and customers."
The offer will be presented by Tuesday to stock market and competition regulators in Europe and the United States, the statement said.
Pechiney shares, which had been suspended most of the day, rose by 1.5% to 46.95 euros after trading resumed.
The stock has now gained about 40% since Alcan declared its first bid on 7 July.
If the takeover is approved, it would create the biggest packaging company in the world, and forge the second-biggest aluminum group after Alcoa in the United States, in terms of sales.
A week ago, the French economy ministry said it would not block the Alcan bid, even though some of Pechiney's aluminium activities are crucial to French defence contractors.
Approval of a deal by European competition authorities is expected on 29 September at the end of a first phase of study.