The 28-year-old has joined the Bulls on a one-year contract from the New Zealand Warriors, for whom he played 144 games in a career stretching back to 1997.
Swann, who played in all three tests against Great Britain last year and won the last of his 26 caps in the Kiwis' 48-6 defeat by Australia in July, is looking forward to joining up with his international team-mates Robbie Paul, Joe Vagana and Lesley Vainikolo at Odsal.
He said: "I am truly excited about joining Bradford Bulls next season."
"It gives me the opportunity to play with a highly-successful club and to continue my association with some former team-mates.
"I find it an honour and privilege to play with such a famous club as Bradford and pledge to play my part in continuing future success."
Swann is the likely replacement for the outgoing Mike Forshaw, who is one of five players to depart from Bradford's Grand Final-winning team.
Bradford, who have lost James Lowes and Daniel Gartner through retirement and parted company with Scott Naylor and Lee Gilmour, are also thought to be close to completing the signing of another New Zealander, centre Toa Kohe-Love, from Hull.