The Saints declined to tender Hardee as a restricted free agent.
Hardee, 26, has spent the past three seasons in New Orleans. He is a core special teams player, having played 114 defensive snaps and 890 on special teams in his career.
Hardee entered the league as an undrafted free agent receiver with the Texans in 2017. The Saints converted him to cornerback when he signed to their practice squad on Sept. 7, 2017.
He has 39 career tackles, one interception and two pass breakups.
Burton, 28, played last season with Washington. He saw action on 68 offensive plays and 177 on special teams.
The Lions drafted Burton in the fifth round in 2015. He spent two seasons there and two in Chicago.
In his five-year career, Burton has 17 touches for 64 yards and a score.