Teams have an off-season training squad of 90 players and must select 53 for the start of the season, the deadline for which was Tuesday.
Rees-Zammit was placed on waivers, meaning other teams could sign him, though it had been expected he would continue his development with Kansas City having initially signed a three-year contract.
Jacksonville were one of several franchises that showed interest in Rees-Zammit after his impressive showing in the IPP pro day in March.
The former British and Irish Lion made his American football debut against Jacksonville earlier this month in the Chiefs’ opening pre-season game.
Each NFL team can have one international player on its practice squad alongside 16 other players.
Practice squad players can work out during the week with NFL teams but are ineligible to play in actual games unless the player is elevated to the regular roster.
Rees-Zammit shocked the rugby world in January when he announced he was quitting Wales and Gloucester to pursue a dream to play in the NFL.
He will now pursue that ambition with the Jaguars in Florida, a team which have a strong presence in the UK.
The Jags will play twice in London this season, facing the Chicago Bears at Tottenham Hotspur Stadium before hosting the New England Patriots at Wembley.
