The Australia international joined Villa in January 2024 and has made two senior appearances.
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Gauci spent the second-half of last season on-loan with Barnsley.
"He's another player with experience of first-team and international football that will provide strong competition in the goalkeeping department here at Vale Park," Vale manager Darren Moore told the club website.
"He will be welcomed straight in to the group and we're all looking forward to working with him this season."