Evans, 26, and the Saints agreed on a seven-year deal announced by the team Wednesday.
The contract is worth $56.7 million and Evans will receive $19 million in the first year and $25.7 million over the first three years of the deal, sources told ESPN's NFL Insider Adam Schefter.
Evans' Philadelphia-based agent, Jerrold Colton, confirmed the deal was the richest contract ever given to an NFL guard.
Evans was a restricted free agent, meaning the Saints owned his rights after a deadline passed for him to sign offer sheets from other teams. However, Evans stayed away from New Orleans' first volunteer offseason workouts while general manager Mickey Loomis and Colton worked on a long-term deal.
"We liked what we saw from him as a small-school prospect in the draft four years ago, and I can say that we've loved what we've seen from him on the NFL level as well," Loomis said in a statement.
Evans, out of NCAA Division II Bloomsburg (Pa.) University, was picked by the Saints in the fourth round in 2006. He has started all 64 games at right guard since being drafted.
"It's important to recognize, with what we do offensively, and the quarterback stepping up in the pocket, to have that size and talent inside the pocket I think is huge for Drew Brees and I think Drew would say the same thing," Saints coach Sean Payton said of the signing. "He's played since his rookie season at an extremely high level and what we've been able to accomplish as a team, offensively, his impact inside of the pocket, what he does, reflects a deal like that."
The Saints allowed 20 sacks last season, fourth fewest in the NFL. New Orleans also led the league in offense for the third time in four seasons.
Run-blocking was Evans' forte at Bloomsburg, which went undefeated in 2005, when Evans was the left tackle and helped starting running back Jamar Brittingham rush for 2,260 yards and 32 touchdowns. While scouts were impressed by Evans' ability to flatten defensive ends and keep tucking downfield to make another block, it was difficult to know how well he'd do against tougher competition.
Evans, a Philadelphia native, had received interest from several Division I schools after his junior year of high school, but a pick-up basketball injury forced him to miss his entire senior season and he wound up with only a partial scholarship to Bloomsburg.
The move will keep one of the Saints' top players in New Orleans through the 2016 season and at least temporarily deflect some of the attention on the Vicodin issues surrounding the team.
The Saints have been dealing with the fallout from a civil lawsuit alleging the team covered up the theft of Vicodin prescription pills by a senior staff member at the team's training headquarters.
The civil suit, seeking damages and back pay, was filed by former security director Geoffrey Santini, who claims he was compelled to resign because of the team's handling of the Vicodin episode.
The Saints have said the allegations are false and represent an attempt by Santini, who resigned last August, to shake down the club. Team spokesman Greg Bensel has said the club will aggressively defend itself in court.
Information from ESPN's NFL Insider Adam Schefter and The Associated Press was used in this report.