Worthington, 51, was confirmed on Monday as successor to Gary Mills, who was sacked after Saturday's home defeat to Bradford, and has appointed former Bury goalkeeper coach Barber and York's youth-team boss Torpey to work alongside him.
"Fred has been with me since Blackpool," said Worthington. "When he was at Bolton he used to come in for a couple of afternoons a week and take the keepers.
"Then I had Fred with me for four and a half years at Northern Ireland. He brings fantastic knowledge and experience to that position and is somebody that works the keepers extremely hard, which I like.
"If you look at (Jussi) Jaaskelainen, ex-Bolton now at West Ham, Fred had a huge part to play in the achievements he's made, so there's a lot of quality there and a lot of football experience, which is good to have alongside you.
"And Steve has been at the club for a number of years.
"He's got local knowledge and knows the players inside out and it was right that we moved him up alongside us.
"It's good experience for him as well and gives him the opportunity of seeing what it's like at the top end. He's a good lad, I've been very impressed with what I've seen so far."
Barber has taken up his new role with Worthington after leaving the Shakers, who he joined at the start of this season.
Bury manager Kevin Blackwell told the club's official website: "I'd like to thank Fred for his time and effort and that he has put into Bury FC, and for the help and assistance that he has given me while I've been here. We all wish him the very best for the future."