Lee Barrett did not make a first team appearance for City but played reasonably well in the reserves for whom he appeared in the Birmingham Senior Cup Semi-Final against Birmingham City.
Pools Director of Football Chris Turner told his club's website: "To get Arran's signature we've have had to sell the Club very well as he had received offers from other Clubs in the South of England and in higher divisions to the one we're going in to.
"We realise that he has not had a great deal of Football League experience but he has great ability and it's a good opportunity for Arran and for us.
"He's got a real presence, commands his area very well and will certainly enhance the goalkeeping department at the Club.'