The person spoke to The Associated Press on Wednesday on condition of anonymity because the agreement has not been announced.
Kruger has started 46 games for Cleveland in the past three seasons, during which he's had 18 sacks, including a career-high 11 in 2014.
Last season, however, he was credited with 27 tackles, his fewest since 2011, and 2½ sacks, his fewest since 2010. When he was released earlier this week, Kruger said the Browns made "absolutely the wrong decision."
His signing with New Orleans was first reported by NFL.com.
The seven-year pro began his career in Baltimore and played for the 2012 Ravens squad that won a Super Bowl. Kruger was credited with nine sacks, an interception and forced fumble during that regular season, and added 4½ sacks and a forced fumble in the playoffs, including two sacks in the Super Bowl.
Kruger also played in the Superdome during his college career, winning a Sugar Bowl when his 2008 Utah team defeated Alabama.
Before adding Kruger, the Saints had several young players vying to fill a pass-rushing role on the opposite side of the line from Pro Bowl end Cameron Jordan.
Hau'oli Kikaha, a second-round draft choice in 2015, was a leading candidate until he tore the anterior cruciate ligament in his left knee during an offseason practice.
Kasim Edebali, who was second on the Saints with five sacks last season, was among the front-runners. Obum Gwacham and Davis Tull also were rotating in at that spot.
Edebali had two sacks in the Saints' preseason opener against New England, but New Orleans has had trouble generating pressure from its defensive front in the past two preseason games, and that was among the issues coach Sean Payton cited as "very concerning" after last week's exhibition loss to Pittsburgh.