Canty received $42 million over six years, according to a person familiar with the contract who requested anonymity because no terms were officially announced.
"He's a veteran defensive tackle with skins on the wall," Giants general manager Jerry Reese said. "He plays hard, he's stout against the run and he has to be accounted for as a pass rusher."
Fred Robbins and Barry Cofield, the starting tackles last season, both have had arthroscopic surgery in the offseason.
"I'm really, really excited to be coming to the Giants," Bernard said. "I wanted to go to a team that has had a lot of success and has a really good defense. That's what the Giants have. It feels good to be part of a great organization. They're a good football team."
Bernard started 55 of 103 regular-season games with Seattle in his seven-year career. He had 282 tackles, 29 sacks and seven fumble recoveries.
The 6-foot-7, 305-pound Canty comes to New York from NFC East rival Dallas. In 2008, he started every game at defensive end for the Cowboys and finished with 37 tackles, three sacks and five passes batted down. He has played both end and tackle in his career.
Terms of his deal were not released.
The Giants were ranked fifth overall in defense last season under Steve Spagnuolo, who left to become coach of the Rams.
Sheridan was promoted from linebackers coach to replace him.
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