The Nashville Predators will have seven days to match Philadelphia's offer. If Nashville declines to match, the Preds will receive a package of draft picks from the Flyers as compensation.
It would mark the second marquee defenceman Nashville has lost this summer. Ryan Suter signed a 13-year, $98 million deal with the Minnesota Wild.
Weber, 26, is coming off an all-star season where he scored 19 goals and 30 assists in 78 games. His career-high came in 2008-09 when scored 23 goals and 50 points. He also won gold with Canada at the 2010 Olympics.
Weber, who made $7.5 million last season with the Predators, would be 40 by the time he played out the contract in Philly.
The Flyers are in need of a top-line defenceman with Chris Pronger's status uncertain. Pronger, who is suffering from long-term concussion symptoms, only played 13 games last season.