The 26-year-old, who is 6ft 9in, has signed a one-year deal and will fight Ross Etheridge for the number one berth at the Crown Ground.
Boss John Coleman told the club’s official website: “It’s something we haven’t had for a long time, as long as I can remember, two goalkeepers having started pre-season.
“It didn’t happen for Jason at York for whatever reason but he went on loan to Alfreton where he enjoyed his football and did well. It’s a chance for him to show what he can do as a league keeper.
“He is big but that’s not the reason he is here. He is keen and keen to work hard and do well and that’s the kind of players we want here.
“There is no number one and number two keeper. It will be whoever is best on any given day and whichever one is chosen, the other will support them. It’s down to them to battle it out.”
Mooney, who has also played for Wycombe and Tranmere, said: “Coming here was a no-brainer for me. It’s the chance to have a clean slate and maybe prove some people wrong. Hopefully I can get regular games because that is the reason I’m in football.
“In my short career so far I think last season is the first one where I didn’t do myself justice. That just makes me want to try even harder this year to show what I can do and help Accrington be successful. That’s what I’m going to do.”