He played most of his 104 games for the Scottish outfit at lock, but has been primarily recruited as a blindside flanker.
Dragons coach Paul Turner said, "He's a ball carrier and a line-out option. We're delighted to secure a young international.
"It was a stroke of luck that he became available as he was due to join Narbonne in France, but the move fell through."
Hall joined Glasgow from Moseley, where he initially attracted the attention of Turner, who was then working with Bedford.
He qualifies for Scotland through a paternal grandfather, and won his solitary cap to date as a replacement against the USA on tour in 2002.
Gloucester have terminated their arrangement with defence coach Dave Ellis and are now looking for a full-time replacement.
Ellis has divided his time between Gloucester and the French national team, with whom he is currently on tour, since joining the club in 2001.
But in keeping with the management revamp taking place at Kingsholm this summer Ellis has been moved on.
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