Welham, 28, spent nine seasons at Hull KR and scored a try on his international debut for the England Knights against Cumbria.
He scored 13 tries in 30 appearances for Hull this year, taking his overall record to 102 tries in 191 games.
He said: "If I can help get Bradford back into the Super League, that's part of the job I'll bring to the club."
"Bradford is a great club with plenty of history and they need to be back in the Super League," Welham added.
"I'll bring experience to the squad, which always helps if we come up against Super League opposition."
Championship side Bradford Bulls have signed centre Kris Welham from Hull Kingston Rovers on a two-year deal.