According to various reports, including one from the Indianapolis Star, the deal is for two years.
Vinatieri connected on 35-of-40 field goal attempts and all 34 PATs last season.
In his eight years with the Colts, the 41-year-old has hit 185 of 219 field goal tries, going 12-of-21 from 50-plus yards, and 99 percent of his PATs, hitting all 146 he has attempted in his last four seasons.
During his 18-year career, which also included 10 years with the New England Patriots, Vinatieri has converted 83 percent of his field goal attempts and 98.5 percent of his PATs.
Notable deaths of 2014 [PHOTOS]