Per NFL Network's Ian Rapoport, it is a four-year deal worth $50 million with $31.5 million guaranteed.
Prior to the new contract, Joseph was signed through the 2018 season.
Injured Vikings quarterback Teddy Bridgewater tweeted his congratulations to Joseph:
The 28-year-old is coming off his best season, as he registered 77 tackles and 4.0 sacks en route to his first career Pro Bowl.
He spent the first four seasons of his career with the G-Men before signing a free-agent deal with the Vikes prior to the 2014 campaign.
Joseph anchors the middle of a strong Minnesota defense as the nose tackle, and he excels at taking on multiple blockers to open lanes for pass-rushers such as Anthony Barr and Brian Robison.
With Joseph leading the way last season, the Vikings ranked third in the NFL in total defense.