In addition, the Patriots placed linebacker Ja'Whaun Benetley and running back Rex Burkhead on injured reserve, and signed defensive back David Jones to the practice squad and released wide receiver Jace Billingsley from the practice squad.
The 29-year-old Barner was signed by the Patriots on Sept. 11 and released eight days later. The 5-9, 195-pounder was drafted by the Carolina Panthers in the sixth round (182nd overall) of the 2013 draft out of Oregon.
Barner went through training camp with the Carolina Panthers this summer and has also had stints with the Philadelphia Eagles and Los Angeles Chargers. He has appeared in 44 regular-season games with one start and has 77 carries for 317 yards and three touchdowns, in addition to 21 receptions for 127 yards. He also has experience as a kick returner.
Simon was a fourth-round draft pick (129th overall) by Baltimore out of Ohio State in 2013. He began his second NFL season on the Baltimore practice squad before being signed to Houston's 53-man roster and was with the Indianapolis Colts last season.
In 54 NFL games, Simon has 99 total tackles, 13 sacks, one interception that he returned 26 yards for a touchdown, four passes defensed, one forced fumble and one fumble recovery.
Last season in Indianapolis, Simon started all nine games that he played in and finished with 27 total tackles, three sacks and one interception.
Jones, 24, was signed by New England as a rookie free agent out of Richmond in 2017. The 6-3, 205-pounder spent his rookie season on the Patriots practice squad and was released last July 23.
Billingsley, 25, has had two stints on the New England practice squad in 2018. The 5-9, 189-pounder entered the NFL as a rookie free agent with Detroit out of Eastern Oregon in 2016. He spent time on the Lions practice squad and 53-man roster in his first two seasons and appeared in two games in 2017 before being released early this month.