Ware's signing comes after the Colts didn't select a running back in the 2019 NFL draft. He joins a backfield led by Marlon Mack. The Colts also have Nyheim Hines, Jordan Wilkins and Jonathan Williams on the depth chart.
The 27-year-old Ware has rushed for 1,580 yards and 11 touchdowns in his four NFL seasons, including the last three with the Kansas City Chiefs.
He joined the Chiefs as a free agent in 2015 after spending parts of two seasons with the Seattle Seahawks. He immediately helped the Chiefs fill the running back void left by a season-ending knee injury to Jamaal Charles by rushing for 403 yards and six touchdowns.
Ware went on to lead the Chiefs in rushing in 2016 with 921 yards. But a preseason knee injury cost him the entire 2017 season and, by the time he returned last year, Kareem Hunt had established himself as the Chiefs' featured back.
When the Chiefs released Hunt late in the season, Ware suffered a hamstring injury and lost an opportunity to reclaim the starting job. By the time he returned, Damien Williams was playing well and had been installed as the featured back.
ESPN's Adam Teicher contributed to this report.