NFL.com's Steve Wyche confirmed the hire.
The Falcons are set to announce the move Monday, the source told ProFootballTalk.com.
Polian was fired by the Colts in January after serving as general manager since 2009. His father, Bill, who had been working in the Indianapolis front office for 14 years, most recently as vice chairman, was also fired on the same day following the conclusion of the Colts' 2-14 season.
Bill Polian was hired as an analyst by ESPN in February.
Chris Polian became the Colts' director of pro scouting in 1998, the same year his father became the team's general manager. The younger Polian became assistant director of football operations in 2001, was named assistant general manager in 2004 and was promoted to the role of general manager in 2009.
Since firing the Polians, Colts owner Jim Irsay has engineered a rebuilding effort that's seen the team part ways with four-time MVP Peyton Manning and select quarterback Andrew Luck with the top pick in the 2012 NFL Draft. Irsay has also hired a new general manager (Ryan Grigson) and coach (Chuck Pagano).
The Falcons' front office has also seen some re-shuffling since the end of the 2011 season, with former director of player personnel Les Snead leaving to become the St. Louis Rams' general manager. The Falcons promoted internal candidates to replace Snead, naming David Caldwell director of player personnel and DeJuan Polk director of pro scouting.
Polian has a long-time relationship with Caldwell, who came to Atlanta from Indianapolis in 2007.