Shockey's deal is worth up to $4 million, with $1 million in guaranteed money, a source told ESPN NFL Insider Adam Schefter.
The 30-year-old Shockey, who was released by New Orleans last week, also had received interest from the Miami Dolphins.
Shockey will be reunited in Carolina with offensive coordinator Rob Chudzinski, who was his position coach at the University of Miami.
"Time for the Next chapter," Shockey wrote on his Facebook page. "This is a great opportunity for me, and I am excited to play football. Lets hope we all have the chance to play this season."
Panthers coach Ron Rivera put an emphasis on acquiring a pass-catching tight end immediately after he was hired in January to replace John Fox following Carolina's 2-14 season.
The flamboyant Shockey could be that guy, although the nine-year veteran has been slowed by injuries the past few seasons.
"We are very pleased to add Jeremy to our football team," Rivera said in a statement. "He is a highly competitive player with a good skill set and a wealth of experience. He should make a solid contribution to our offense."
The 6-foot-5, 251-pound Shockey made the Pro Bowl in four of his first five seasons in the NFL with the New York Giants, but also was known for brash comments and feuds with coach Tom Coughlin.
He was traded to New Orleans before the 2008 season and caught a key touchdown pass in Saints' Super Bowl victory a year later. But Shockey labored through injuries in all three seasons in New Orleans and the Saints cut him loose with $4.2 million due to him in 2011 in the final year of his deal.
If he can stay healthy, Shockey, who had 41 catches for 408 yards and three touchdowns in 13 games last season, will provide a target at tight end not seen in years in Carolina.
Fox used the tight end mostly as a blocker and the Panthers had Jeff King, Dante Rosario and Gary Barnidge play there last season in a platoon. King and Rosario are potential free agents, although the Panthers placed restricted free-agent tenders on both players Wednesday.
What remains uncertain is who will be throwing Shockey the ball this season. Rookie Jimmy Clausen was 1-9 as a starter in 2010 and the Panthers are considering signing a veteran or perhaps even selecting a quarterback with the No. 1 overall pick in next month's draft.
Information from The Associated Press was used in this report.