A source told ESPN.com's John Clayton that McDougle receives a one-year, $1 million deal.
The Super Bowl champions lost seven-time Pro Bowler Michael Strahan to retirement in June and then had two-time Pro Bowler Osi Umenyiora sidelined with a season-ending knee injury a little more than a week ago in a game against the Jets.
New York moved Mathias Kiwanuka from linebacker back to defensive end days after Umenyiora was hurt.
A first round pick in 2003, McDougle was cut by Philadelphia on Saturday. He played in 33 games in five seasons and had three sacks. He missed all of last season with a triceps injury and was out for all of 2005 after being shot in the abdomen during a robbery during the offseason.
"It is great -- defending Super Bowl champs -- I look good in blue," McDougle said. "I feel good to be here, staying in the division, so not really much of a difference as far as guys you are going against, and I just feel good to be here, to be wanted, and I am just looking forward to doing some good things on this defense."
Coming to the Giants, McDougle will played under defensive coordinator Steve Spagnuolo, who was a linebacker and defensive backs coach with the Eagles until being hired by New York.
"Coach Spags has done a good job here," McDougle said. "He really gets after it and kind of put his own niche on kind of the defense that we were running there in Philly. It is good for me because there is a lot of movement, which allows for guys like me a chance to kind of move and get after the quarterback a little bit."
To make room for McDougle on the 53-man roster, the Giants waived defensive tackle Rodney Leisle.
Information from The Associated Press was used in this report. Senior writer John Clayton covers the NFL for ESPN.com.