Collins, 38, could be called upon to sub for Manning, who has never missed a game in his 13-year career but has not yet recovered sufficiently from a May 23 neck procedure for a disk-related issue.
Collins led the New York Giants to the 2000 Super Bowl and has toiled the past five seasons for the Tennessee Titans. He had announced his retirement in July.
"It is a good opportunity to have Kerry become part of the team," Colts Coach Jim Caldwell said. "He is a veteran quarterback who has started many games and he brings dimension and depth to the quarterback position, which will be helpful."
Collins has tossed for 40,441 yards with 206 touchdowns and 195 interceptions in his long career.
He appeared in 10 games last season for the Titans, throwing for 1,823 yards with 14 touchdowns and eight interceptions.