A league source told ESPN NFL Insider Adam Schefter that the Vikings used the "non-exclusive" franchise tag on Greenway.
Greenway has led the team in tackles for three straight seasons. He was chosen the team's 2010 defensive MVP and had 144 tackles. He will be entering his sixth season, including a rookie season that he sat out with a knee injury.
If the franchise tag designation stays in its current form in the next collective bargaining agreement, Greenway stands to make nearly $10 million next season. But the Vikings would like to get a long-term deal done with the 28-year-old, which would negate that number.
"Chad's an important part of our team and his play speaks for itself," coach Leslie Frazier said in a statement on the team's website. "He's productive and has continued to improve each year he has been in the NFL. "He's a leader for us in the locker room and on the field."
Many players chafe at the designation, viewing it as an obstacle in their way of a long-term contract with big guaranteed money. But in a statement issued by the team, Greenway said he was "happy to know that the Vikings value me enough to make this move."
He said he looked forward to playing for Frazier, defensive coordinator Fred Pagac and new linebackers coach Mike Singletary next season, and well into the future.
"It's been a goal of mine since getting drafted to play with the Vikings my whole career," he said. "I think we're one step closer to that now."
The decision to tag Greenway means that neither wide receiver Sidney Rice nor defensive end Ray Edwards will be tagged and each potentially could become a free agent depending on what happens with the ongoing collective bargaining agreement talks. The current CBA will expire at the end of the day on March 3 and owners might lock out the players if a new deal isn't signed.
Since the Vikings didn't use the "exclusive" tag, Greenway can negotiate with other teams. If he receives an offer, the Vikings can either match the other club's offer or receive two first-round draft choices as compensation.
Teams have until Thursday to use their franchise tag. So far, only quarterbacks Peyton Manning and Michael Vick have received exclusive franchise tags, barring them from talking to other teams during the free-agency period.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.