Joseph, 27, spent 2012 with the Bulls after earning a contract with them following a trial, having opted to give full-time rugby another try.
He previously played for Swinton, Oldham, Halifax and Hull KR in the Championships, and has been in pre-season training with the Vikings.
The Wales international, capped seven times, made six appearances for Bradford last season.
Former Wigan back-rower Matthew Sarsfield was released from the last year of his contract at Huddersfield last month, having failed to make a single first team appearance.
Both players have been named in Widnes’ 21-man squad for their Boxing Day friendly against local rivals Warrington.
Widnes squad: Allen, Craven, Cahill, Davies, Dean, Flynn, Gerrard, Gilmore, Gore, Hanbury, Isa, Joseph, Kavanagh, Lawton, Leuluai, Marsh, Mellor, Owens, Phelps, Sarsfield, Winterstein.