Bailey's deal will have a maximum value of $7 million, a league source tells ESPN's Adam Schefter.
Bailey, 35, is the same age as Saints quarterback Drew Brees, giving New Orleans a likely Hall of Famer on each side of the ball.
"We are excited to be able to add a future Hall of Fame player with the addition of Champ Bailey," Saints general manager Mickey Loomis said in a statement released by the team. "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. 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 was released by the Denver Broncos earlier this offseason because of a lofty price tag and declining production. But the 12-time Pro Bowler is said to be healthy after being plagued by a foot injury last season, ESPN NFL Insider Adam Schefter reported earlier this week.
Bailey will compete for a starting job in New Orleans opposite Keenan Lewis, the team's No. 1 cornerback.
"I'm excited," the 35-year-old Bailey told the team's official website. "Last year was one of those years that I just couldn't get over the fact of being hurt and grind my way through that. It was a tough, up-and-down year.
"... I'm still hungry. I've still got that drive to go out there and be the best and that's why I'm still putting them on, and the Saints gave me an opportunity. I'm going to try to be a part of something special."
The Saints' defense emerged last year as one of the top young defensive units in the NFL. And now they've made two big splashes in free agency, previously signing standout safety Jairus Byrd last month.
Bailey could also play a hybrid cornerback-safety role in the Saints' nickel and dime packages. The 6-foot, 192-pounder said earlier this year that he would consider switching to safety if needed. And the Saints could be thinner than expected at safety if they lose restricted free agent Rafael Bush to the Atlanta Falcons.
"I have a little more to my game, I believe, especially mentally," Bailey told the Saints' website. "I can see things a lot easier. A lot of things come up that I've had experience with. That only helps your game. I'm using that to my advantage as much as possible."
The Saints were about $2 million under the salary cap to begin the day Friday -- though that included $1.4 million that was charged for the qualifying offer they made to Bush.
Bailey is one of the NFL's all-time great defensive backs, with 52 interceptions in a 15-year career spent with the Broncos and Washington Redskins. He just appeared in his first Super Bowl with the Broncos this past season.
However, the Broncos decided to let Bailey go before he was set to cost $10 million against their salary cap this season because his skills have started to show signs of decline in recent years.
Last year, Bailey played in a career-low five regular-season games because of the injury before returning for the playoffs. In 2012, he was beat for two rare long touchdown passes in a playoff loss to the Baltimore Ravens.
Bailey made it clear that he wanted to continue playing, though. And now he'll keep chasing that elusive first Super Bowl ring in New Orleans.