"To be able to come back here is amazing," Ginn said in a statement released by the team. "It's a blessing to have a family like this that is willing to give me another opportunity to be on their ball club."
Ginn also posted a photo of himself signing the contract on his Instagram account.
With the deal, Ginn will return to Carolina, where he played in 2013 and caught a career-best five touchdown passes.
"We are very pleased to have Ted back," general manager Dave Gettleman said in the statement. "He gives us big-play ability as a punt returner and a wide receiver. He still has his speed. He can still fly."
The Arizona Cardinals released Ginn last month, freeing $2.5 million of cap space.
Ginn, who turns 30 in April, had an underwhelming 2014 as Arizona's punt and kick returner and its fifth receiver. His highlight came in Week 2, when he returned a punt 71 yards for a touchdown against the New York Giants. Beyond that, Ginn struggled with deciding whether to bring kickoffs out of the end zone.
His 277 punt-return yards were the fewest of his career when he was his team's primary returner since his rookie season in 2007. Ginn's 417 kickoff-return yards were the second fewest of his career. He did notch a punt-return touchdown in 2014, however, the fourth of his career.
Ginn finished 2014 with 190 receiving yards on 14 catches. Both were the second fewest of his career in seasons where he was an active receiver.
His single-season career bests for receptions and yards came in 2008 with the Dolphins, when he had 56 catches for 790 yards.
ESPN.com Cardinals reporter Josh Weinfuss contributed to this report.