The deal is for 3 years and $27 million, a source told ESPN's Josina Anderson.
Piece is expected to fill the void left by nose tackle Linval Joseph, who was released Friday to free up $10.55 million in cap space for Minnesota.
In a statement from the team, general manager Rick Spielman left the door open for Joseph to return, stating the Vikings would "remain in communication as all parties navigate free agency moving forward." On Wednesday, Joseph agreed to terms of a two-year deal with the Los Angeles Chargers, a source confirmed to ESPN.
Finding a replacement for Joseph at nose tackle became a strong priority for the Vikings after the 31-year-old was cut. The responsibilities placed on a nose tackle in Zimmer's defense require a specific fit, given most 4-3 fronts are typically one-gap schemes, with the exception of how the Vikings played Joseph over the last six years.
Pierce presents the type of strength required to play the position. His pedigree against the run is likely why Minnesota saw it as an ideal fit. The Vikings also have Jaleel Johnson and Armon Watts, who filled in at nose tackle on a rotational basis last season. Pierce, who turned 27 in November, has gone from being an undrafted rookie from Samford in 2016 to one of the top young run-stuffers in the league with the Ravens. His 151 tackles in that span are the third-most among defensive tackles in the AFC North.
The 345-pounder was a cog for the NFL's No. 5 run defense this past season, using his massive lower-body strength to seal off the interior alongside Brandon Williams. With those two on the field, Baltimore held teams to 3.5 yards per carry over the past two seasons. Without them, the Ravens gave up 4.9 yards per carry over that same span.
The Ravens knew they would not be able to re-sign Pierce because of their huge investment in Williams, who is scheduled to make $9.25 million in each of the next two seasons. They also already signed Pierce's replacement Monday when they added Michael Brockers, a free agent from the Los Angeles Rams.
Pierce weighed 390 pounds when he reported to last year's June minicamp, and he was sent off the practice field by coach John Harbaugh. But Pierce lost 30 pounds by the start of training camp and finished the season with 35 tackles.
ESPN's Jamison Hensley contributed to this report.