Bailey was released by the Broncos following the Super Bowl due to a high price tag and concerns over his fitness after he missed a large chunk of the 2013 season.
However, the 12-time Pro Bowler, who is widely regarded as one of the greatest cornerbacks in NFL history, is understood to have overcome those injury problems, prompting the Saints to sign him to a deal reportedly worth up to $7m (£4.2m).
"We are excited to be able to add a future Hall of Fame player with the addition of Champ Bailey. His career accomplishments mirror that of his high character and he's a very prideful and competitive player who we believe will add to our defense," Saints general manager Mickey Loomis said in a statement.
"Having spent time with him recently and in our discussions with him, I know that he's thrilled to be joining the New Orleans Saints and starting a new chapter in his professional life."
Bailey, 35, has recorded 52 interceptions in his 15-year career since being chosen seventh overall in the 1999 NFL Draft.