Canty, according to a source, received a six-year, $42 million contract. Another source told ESPN.com's Matt Mosley that $17.25 million of the deal is guaranteed.
On Saturday, the Giants signed former Seahawks defensive tackle Rocky Bernard for around $4 million per year, according to a source.
Even though Canty played end in the Cowboys 3-4, he is expected to play tackle for the Giants. Sensing Canty was going to have a market in the $7 million per year range, the Cowboys didn't have the room to keep him.
The former fifth-round pick started 48 consecutive games over the past three seasons and had two starts in his rookie year in 2005. Last year, he had 37 tackles and three sacks for the Cowboys.
Canty had narrowed his decision Sunday to the Giants and the Packers. He had a tentatively scheduled a trip to Seattle for Monday, but he was notified early Sunday morning that the Seahawks were going to sign Packers defensive tackle Colin Cole.
Senior writer John Clayton covers the NFL for ESPN.com. Matt Mosley covers the NFC East for ESPN.com.