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.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys