The Times-Picayune reported his deal could be worth more than $11 million with incentives, including more than $5.7 million in guaranteed money.
The 6-foot-2-inch, 214-pounder is the fifth first-round pick to sign an NFL contract this year.
"I'm very happy," Meachem told the New Orleans newspaper. "Everything went smooth (and) it wasn't a rough process. I just wanted to be in camp to let my teammates and coaches know that I want to play."
Meachem caught 71 passes for 1,298 yards and 11 touchdowns in the 2006 season.
After red-shirting in 2003, he finished his UT career with 17 touchdowns on 125 receptions for 2,140 yards.
"Robert has worked hard since he joined our team and we expect more of that to come in training camp and beyond," said General Manager Mickey Loomis on the team's Web site after Tuesday's signing.