NFL Network's Ian Rapoport reports the deal is worth $3 million.
Hasselbeck has served as Andrew Luck's backup for the last two seasons, appearing in seven games and throwing for 431 yards and two touchdowns with one interception and a 66.1 percent completion percentage.
The 39-year-old started his career with the Green Bay Packers in 1999 before spending 10 years as the starter for the Seattle Seahawks. He was named to the Pro Bowl in 2003, 2005 and 2007 and was first-team All-NFC in 2005.
Hasselbeck was coming off a two-year deal he signed with Indianapolis in 2013.
- Molly Geary