The Falcons will receive no return on the guaranteed $2.5 million salary in 2008 for the 36-year-old Horn.
Horn said he wished he could have produced better numbers for team owner Arthur Blank.
"It's a sense of sadness because after every game last year and after the first two preseason games I had to look at Mr. Blank and know that he deserves a winning team and he deserves a championship," Horn told the Associated Press. "I was here and couldn't make it happen. It's kind of sad for me leaving."
Horn was a disappointment in 2007, when he caught only 27 passes for 243 yards and one touchdown after signing a four-year, $14.5 million deal.
Horn sat out voluntary workouts, did not play in the team's first two preseason games because of a hamstring injury and asked to be traded.
"I'm 100 percent ready to run," Horn said Tuesday when asked about the injury.
Horn's agent, Ralph Vitolo, said Dallas, Jacksonville, Seattle and Tennessee could have a need for a veteran receiver.
"Now we're calling these teams and kind of narrowing the scope," Vitolo told the Associated Press. "Joe has been so productive. Somebody like Joe and a team with a need should be a perfect fit."
Vitolo called Horn's hamstring injury "just a nagging thing."
"It was just mentally wearing him down more than physically," he said.
Horn, drafted by Kansas City in 1996, spent seven years with the New Orleans Saints. His production declined his last two years with the Saints, but still the Falcons offered $7.5 million in guaranteed salary and bonus when looking for help at wide receiver in Bobby Petrino's pass-oriented offense last season.
"That's what locked him in with Atlanta," Vitolo said of the guaranteed money.