They agreed to a one-year deal worth up to $3 million, his agent, Drew Rosenhaus, told ESPN's Adam Schefter.
It's a birthday present of sorts for Alexander, who turned 27 on Tuesday.
Alexander, who played college football nearby at LSU, proved to be a good fit for the Saints after they acquired him in a trade with the San Francisco 49ers last November. The 6-foot-1, 227-pounder started seven games for New Orleans and had 27 tackles, a forced fumble and two fumble recoveries. His season ended in December, however, when he suffered a torn Achilles tendon in a Christmas Day victory over the Minnesota Vikings.
The Saints released Alexander in March before he was due to make $13.4 million in salary and bonuses this year. But clearly they kept the door open, and they brought him in for a workout last month after he was healthy enough to resume football activities.
The Saints are suddenly crowded at the linebacker position after they drafted Pete Werner in the second round this year and Zack Baun in the third round last year. And it's a position where they typically play only two linebackers at a time, with Demario Davis locking down one of those spots. But Alexander, who is particularly valuable on passing downs, adds to their overall depth and versatility after they lost some key pieces at cornerback and along the defensive line during a salary-cap purge this offseason.
The Saints have been filling out their depth throughout the first week of training camp after they cleared out more than $10 million in cap space late in the summer. They have also recently signed cornerbacks Brian Poole, Prince Amukamara and KeiVarae Russell; running back Devonta Freeman; receiver Chris Hogan and guard J.R. Sweezy.
Alexander, who was originally drafted by the Tampa Bay Buccaneers in the fourth round out of LSU in 2015, made the Pro Bowl in 2017. He has started a total of 66 games in his career with 471 tackles, 8.5 sacks, 7 interceptions and 9 forced fumbles.
The 49ers signed Alexander to a four-year, $54 million contract as a free agent in 2019, but he was limited during the 2019 season by a torn pectoral muscle before returning for their playoff run. He played in five games for the 49ers in 2020 but was sidelined by a high-ankle sprain at the time he was traded.