The 28-year-old Greenway has led the team in tackles for three straight seasons. He was chosen the team's 2010 defensive MVP and had 149 tackles. He will be entering his sixth season, including a rookie season that he sat out with a knee injury.
Greenway stands to make nearly $10 million next season after signing the tender.
"Chad's an important part of our team and his play speaks for itself," coach Leslie Frazier said last week after the Vikings placed the tag on Greenway. "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 last week, 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."
Information from The Associated Press was used in this report.