The 54-year-old, who has been at the Riverside since 2001 and replaces Terry Gennoe who quit last month due to a long-term back problem.
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Barron: "I am delighted to be here and cannot wait to get down to work with our four keepers.
"I was very happy at Middlesbrough, but this is a great opportunity and I am very much looking forward to it.
"Of course I know all about the quality of the goalkeepers at this club and it is great to work with top players.
"It is not just Shay (Given) and Steve (Harper), but Fraser Forster and Tim Krul are also very promising young goalkeepers.
"The potential at this club is huge and I am looking forward to being part of it."