Under the terms of the new deal, Greenway's base salary for 2015 will be reduced from $7 million to $3.4 million, according to Yates.
Greenway will earn $1 million in guaranteed money and can make an additional $600,000 from bonuses, Yates reported.
The restructuring will create $3.2 million in cap space. Next season is the final one of Greenway's deal.
Greenway, 32, has spent eight seasons with the Vikings since being selected in the first round of the 2006 draft.
He had played in every regular-season game between 2007 and 2013 (and started all but one) before missing four games last season.
Greenway, a two-time Pro Bowler, recorded 93 tackles last season.