Jones, 33, began his career at Middlesbrough and played 75 times for Boro before joining Liverpool in 2010.
He made 27 appearances in five seasons at Anfield, the last coming in a Premier League win at Burnley in December, and was released in June.
Jones will go into Bradford's squad for Tuesday's home game with Gillingham.
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League One club Bradford City have signed Australia international and ex-Liverpool goalkeeper Brad Jones on a one-year contract.