ESPN have reported that his contract could work out as much as $47.5 million with the Packers' NFC North rivals and the 29-year-old is guaranteed $18 million.
Jennings had three consecutive 1,000-yard seasons from 2008-10 and nearly did so again in 2011 when he missed three games due to a sprained left knee.
The player made only 10 appearances for the Packers last campaign because of a torn lower abdominal muscle, but he feels he can still produce the goods at the highest level.
"I can definitely still do it," said Jennings, who will turn 30 in September. "I can definitely still make plays and be as exciting as I was in my earlier years."
Jennings won one Super Bowl and went to two Pro Bowls during his time at Lambeau Field, as he became quarterback Aaron Rodgers' top receiver.
However, his age and recent injuries meant the Packers were never going to hand him a huge salary, in what could be his last NFL contract.
With Jordy Nelson, James Jones and Randall Cobb all stepping up last season, Green Bay also finds itself with a healthy crop of receiving talent and all those factors meant Jennings' exit was inevitable.
Minnesota also needed a star wideout after Percy Harvin left for Seattle, and opted to bring Jennings across the divide from their NFC North rivals.
The Vikings have also signed quarterback Matt Cassel - who was cut after four years in Kansas City - to be Christian Ponder's back-up next season.