The deal first was reported by ESPN.
Freeney, a first-round draft pick in 2002, missed the Pro Bowl this year for the first time since his rookie season. He was held to a career-low 5 1/2 sacks while fighting shoulder and leg injuries, the only time he has been under double digits in sacks.
His long-term deal would be the Colts' biggest investment in their defense for what has long been an offensive-oriented team.
Under the franchise tag, Freeney had been guaranteed $8,644,000, the average salary of the top five defensive ends next season.