The team didn't disclose the terms of the contract.
Smith, who turns 33 in July, ranks fourth in Saints history with 67.5 career sacks. He missed last season after tearing his ACL in August and had been the longest tenured member of the Saints before his release Feb. 12.
The Patriots, who run a multiple-front defense, have a notable drop-off on their defensive end depth chart after starters Chandler Jones and Rob Ninkovich, who each played more than 95 percent of the defensive snaps in 2013.
Smith, assuming he returns to health, could help fill that void while also factoring into sub packages, which the Patriots were in 67 percent of the time last season. At 6-foot-3 and 282 pounds, he is a power rusher with experience in big games.
Smith was due $11.55 million in salary and bonuses in 2014, which contributed to the Saints' decision to release him.