"Still got to take a physical but it's a done deal," Sanders wrote in a text message to Anderson.
Sanders will get a $16-million contract worth up to $19 million, Adam Schefter of ESPN reports.
The two-time Pro Bowler spoke with the Dallas Cowboys and Green Bay Packers but preferred the Saints, Schefter adds.
New Orleans was expected to add new wideouts this offseason to address an area of need.
Michael Thomas, the 2019 Offensive Player of the Year, was the only Saints wide receiver to top 450 receiving yards last season, while Ted Ginn Jr. ranked second among the team's wideouts with only 30 receptions. With Ginn currently a free agent, Tre'Quan Smith was expected to line up as New Orleans' No. 2 wide receiver in 2020.
Sanders was an important asset for the San Francisco 49ers after they acquired him in a midseason trade with the Denver Broncos. The 33-year-old amassed 36 receptions for 502 yards and three touchdowns in 10 regular-season games with the 49ers.
Overall, he finished 2019 with 869 yards and five touchdowns - both his best marks since 2016 - on 66 catches. He added another five catches for 71 yards in three playoff games during San Francisco's run to Super Bowl LIV.
New Orleans will be Sanders' fourth NFL stop in 11 career seasons. He played for the Pittsburgh Steelers from 2010-13.