Terms of the deal were not disclosed.
The Lions decided not to re-sign Reiff after making Rick Wagner one of the league's highest-paid right tackles, earning $8 million in 2016 – the same he earned in all of the previous four seasons combined.
Reiff was a first-round pick out of Iowa in 2012. In five seasons with the Lions, he started 69 of a possible 77 games.
Last season was Reiff's first at right tackle after manning the left tackle position for the Lions from 2013-2015. Where Reiff will land along the offensive line is not certain. The Vikings have holes at both left and right tackle after Matt Kalil signed a deal with the Carolina Panthers.
The Vikings also have an opening at running back after allowing Adrian Peterson to become a free agent. Minnesota has shown an interest in former Green Bay running back Eddie Lacy, who will visit the Vikings in the next couple of days.
The former Alabama running back took the NFL by storm when he entered the league in 2013. He rushed for 1,178 yards and 11 touchdowns that season and followed it up with 1,139 rushing yards and nine touchdowns.
But being out of shape and injuries have limited his play and now he is looking for a new beginning.