The 49ers, Broncos and Texans were also in the mix to land the 30-year-old Betts, but he preferred the opportunity and the money offered by New Orleans.
The Saints have been looking for a back to replace Mike Bell, who left as a restricted free agent during the offseason. The Saints lost running back Lynell Hamilton for the season with a knee injury earlier in the preseason.
Betts spent eight seasons with the Redskins.
John Clayton covers the NFL for ESPN.com.