Joseph's deal comes one day after the Vikings re-signed defensive end Everson Griffen to a five-year deal worth $42.5 million, according to a league source.
A second-round pick by the New York Giants in 2010, Joseph is still just 25 and has been productive the past couple years. His primary responsibility as a defensive tackle in the Giants' 4-3 front has been to stop the run, and he's excelled at it. But he also has an ability to generate pressure on the quarterback from the interior of the line, recording seven sacks and two forced fumbles over the past two seasons.
Joseph missed the Giants' Week 5 game against the Eagles last season with an ankle injury but has otherwise been durable. That is the only game he has missed in the past three seasons.
Joseph said late in the season that he'd like to stay with the Giants, but he also made a reference to the five-year, $54.75 million contract defensive tackle Geno Atkins signed with the Bengals this past year to illustrate the extent to which he was looking forward to free agency.
ESPN.com Giants reporter Dan Graziano contributed to this report.