The deal is for 14 years and is worth about $110 million, a source confirmed to ESPN.com. Weber, 26, will receive $56 million in the first four years of the deal, a source told ESPN The Magazine NHL Insider Craig Custance.
In the first four years of the contract -- when he'll earn $14 million per year -- $13 million per year is designated as a signing bonus, with an additional $1 million in salary, the source told Custance.
A restricted free agent, Weber has spent his entire career with the Nashville Predators, who have seven days to match Philadelphia's offer, which was first reported by TSN of Canada.
If the Predators decide not to match the offer, they would receive four future first-round draft picks from the Flyers, according to TSN.
"We have stated previously that, should a team enter into an offer sheet with Shea, our intention would be to match and retain Shea," Predators general manager David Poile said. "Due to the complexity of the offer sheet, we will take the appropriate time to review and evaluate it and all of its ramifications in order to make the best decision for the Predators in both the short and long-term."
A three-time All-Star and the Predators' captain the past two years, Weber recorded 19 goals and 49 points this past season while anchoring one of the NHL's top defensive teams.
"We didn't go actively looking for an offer sheet," said Jarrett Bousquet, Weber's agent. "But when we spoke with Philadelphia, it seemed to be a right fit there.
"I think at the point, (Weber) is really in a good situation. I think he wants to explore his options. I don't think he would sign an offer sheet unless you were hoping you were able to go to that team."
"Things changed in Nashville July 4," Bousquet said. "The next four or five days we had to look at different options."
The Predators said they had the money to keep Weber and Suter after signing goalie Pekka Rinne to a seven-year, $49 million deal last November. But Poile couldn't keep Suter in town despite team officials thinking they had a good chance to keep their top draft pick in 2003. The Wild not only snagged Suter, but also agreed with forward Zach Parise, Suter's good friend who left New Jersey for a similar deal to Suter's, a month after leading the Devils to the Stanley Cup finals.
Clearly, the Flyers are in a position of need. They have watched teams around them in the East get better and are still smarting from consecutive second-round playoff exits. And last summer, general manager Paul Holmgren pulled off stunning deals to get rid of high-priced forwards Mike Richards and Jeff Carter. The two ended up helping Los Angeles to the Stanley Cup last month.
The Flyers were exposed on defense this past season in a five-game, Round 2 playoff series loss to New Jersey. They since have lost defenseman Matt Carle, who snared a six-year, $33 million deal with Tampa Bay.
Weber would fix a lot of those problems.
Weber also would fill the void left by Flyers defenseman Chris Pronger. Pronger -- a key cog in the Flyers' run to the 2010 Stanley Cup finals -- has been battling concussion problems and missed most of last season. He finished with one goal in 13 games.
The highly coveted Weber also was interested in the Rangers and visited New York recently, multiple sources confirmed to ESPNNewYork.com's Katie Strang. He also paid visits to San Jose and Detroit.
"(Philadelphia) just seemed to be a better fit than New York," Bousquet told Strang.
Bousquet said the main deterrent for Weber in terms of New York was the prospect of living in Manhattan.
"He's a small-town guy, and it's a huge city," Bousquet said. "With New York, it was nothing personal. He thought everything, from the ownership to the hockey operations to the coaching was unbelievable. (Philadelphia) just seemed to be a better fit at this time in his career."
Weber has 99 goals and 164 assists in his seven-year NHL career.
Information from ESPNNewYork.com's Katie Strang and The Associated Press was used in this report.