He'll compete for a spot on the Giants' depth chart at running back, a position that is led by starter Saquon Barkley, who is returning from a torn ACL suffered last season, and includes Devontae Booker and newly signed veteran Corey Clement, among others.
Armstead, 24, was twice placed on the reserve/COVID-19 list last season. He spent 19 days on the list the first time, then dealt with a groin injury and another illness before going back on the list. Players are placed on the reserve/COVID-19 list if they test positive for the virus or have been in close contact with someone who has.
Armstead was a fifth-round pick of the Jaguars in 2019 and ran for 108 yards on 35 carries as a rookie.
The Giants released quarterback Joe Webb, who appeared in two games last season on special teams, in a corresponding move.
ESPN's Michael DiRocco contributed to this report.