Moore had signed with the Falcons on Friday to compete for the No. 5 wide receiver spot. He played 10 seasons, finishing with 389 receptions for 4,816 yards and 44 touchdowns.
Moore reflected on his career in a Facebook post, writing that he "always prided myself in playing for the right reasons and respecting the game. At this point if I were to continue to play I would no longer be doing that."
"I've got a lot of respect for him as a man,'' Falcons coach Dan Quinn said. "I thought it was real admirable, his approach. What a pro to say, 'If my heart is not in it, I want to make sure I'm not taking the opportunity from somebody else.' I thought, 'Man, what a classy guy.'
"I wish him the best. A guy like that you know is going to be very successful past football.''
Moore, who will turn 33 on Aug. 31, had a career revival with the Lions in 2015 after signing a one-year deal with Detroit last offseason. He had 29 catches for 337 yards and four touchdowns as the team's No. 3 receiver.
The longtime Saints stalwart spent nine seasons in New Orleans and was a key receiver on the franchise's Super Bowl-winning team in 2009.
"He's one of the best receivers that has played here. The thing that stands out, man, he was consistent, and he would come up big on third down, in the red area. Had a tremendous career," Saints coach Sean Payton said Monday.
Moore's best statistical seasons were 2008 and 2012. He caught 79 passes for 928 yards and 10 touchdowns in 2008, and hauled in 65 receptions for 1,041 yards and six scores in '12.
He entered the NFL as an undrafted free agent in 2005.
"You're always fond of those guys that start on first base. And Lance -- he started in the dugout. Played over in Europe, then on a practice squad, then worked his way into the starting lineup, was a part of our championship run," Payton said.
"The game will miss a guy like him. He's outstanding."
Between New Orleans and Detroit, Moore spent one season in Pittsburgh, where he caught 14 passes for 198 yards and two touchdowns.
ESPN's Vaughn McClure, Mike Triplett and Michael Rothstein contributed to this report.