According to the New Orleans Times-Picayune, the school will make it official on Monday.
Johnson, a New Orleans native, has been the receivers coach with the Saints since 2006 after a lengthy tenure as a collegiate assistant. He spent nine seasons at Miami-Florida, helping the Hurricanes to nine bowl games and the 2001 national championship, and was also an assistant at California, SMU, San Diego State and Idaho.
Saints quarterback Drew Brees endorsed Johnson's move to Tulane after Sunday's game against Detroit.
"I think he's going to be great," Brees stated. "Curtis Johnson has a lot of relationships here in New Orleans. He's been around the football field here a long time. That's one thing he's great at -- he has a ton of relationships. He's been a great part of our offensive staff here over the last six years. He's been a lot of places and coached a lot of big-time players. It's great for Tulane's program. They got a great coach in Curtis Johnson."
Tulane was just 2-11 this past season. Bob Toledo resigned after a 2-5 start in his fifth year and Mark Hutson guided the team in its final six games -- all losses. The Green Wave concluded the season with a 10-game losing streak.
Toledo was just 15-40 during his 4 1/2 seasons with the Green Wave, who haven't had a winning season since 2002.