Audel, 30, ended a two-year association with the Magpies at the end of last season having made 53 appearances in all competitions.
The French centre-half has also played for Triestina and Pisa in Italy as well as Macclesfield, Crewe and Lincoln.
He is the National League Bluebirds ninth signing of the summer.
Find all the latest football transfers on our dedicated page.
Barrow have signed defender Thierry Audel on a one-year deal with an optional second year, following his release by Notts County.