The 30-year-old former Great Britain forward had been thought to have signed a deal with the Warriors, but will instead replace Marcus Bai who offered suddenly retired from rugby league last month.
"I am delighted to have been given the opportunity to come back to Bradford," said McAvoy, who first joined Bradford in 1998 before switching codes to play for Saracens.
"I thoroughly enjoyed my time with them before and enjoyed a lot of success. It's great that I will once again be playing in front of the tremendous Bradford supporters."
McAvoy made his return to league in 2004 with Salford City Reds before spending some time at Leeds Rhinos, and being part of the Wigan team that dragged the Warriors out of relegation trouble.
"I am absolutely delighted to have the opportunity to strengthen our squad," said coach Steve McNamara, who is guiding the Bulls through his first pre-season having taken control of the side in April last year.
"The loss of Marcus Bai was a shock to us and to be able to strengthen our backline with a player who is a good person, a good athlete and a player who played with a lot of confidence at the back end of last season is a big bonus for us.
"It's good to have him on board and he will stiffen the competition for places this year."