Each team has an offseason training squad of 90 players, and must select 53 to start the season, with the deadline for selection being Tuesday.
He was placed on waivers, meaning he could be recruited by other teams, but he originally signed a three-year contract with the Chiefs and was expected to continue developing in Kansas.
Jacksonville was one of several franchises to express interest in Reese-Zammet following his impressive showing at the IPP Pro Day in March.
The former British and Irish Lion made his football debut in Kansas City’s preseason opener against Jacksonville earlier this month.
Each NFL team is allowed to have one player signed through the IPP program and 16 other players on its practice squad.
Practice squad players are allowed to train with NFL teams during the week, but are not eligible to play in actual games unless they are added to the regular roster.
Rees-Jammit shocked the rugby world in January when he announced he would be leaving Wales and Gloucester to pursue his dream of playing in the NFL.
He will now pursue that ambition with the Jaguars in Florida, according to sources reported by ESPN., external.
The Jaguars franchise has a strong presence in the UK. They play twice in London this season, taking on the Chicago Bears at Tottenham Hotspur Stadium and then the New England Patriots at Wembley.