The 25-year-old, who arrived from A-League side Adelaide United in February 2024, made two appearances for Villa in the EFL Cup last term.
Gauci also played seven times on loan at Barnsley earlier this year, but saw his temporary stay at Oakwell disrupted by injury.
In total, Gauci made seven appearances for the Tykes, keeping two clean sheets. His loan departure has possibly increased the likelihood of World Cup winning goalkeeper Emi Martinez staying at the club this summer.
There had been speculation surrounding Martinez's future after spending the past five seasons at Villa Park - registering 70 clean sheets in 212 matches across all competitions.
Villa signed 34-year-old Dutchman Marco Bizot from Brest at the beginning of the window, but Gauci's exit means the goalkeeping department has been cut to just three.
Martinez, who was nominated for the Yashin Trophy (an award he has won twice), has been a standout performer during pre-season.
The 32-year-old pulled off a string of excellent saves as Villa rounded off pre-season with a 2-0 win over Villarreal on Sunday night.
Ollie Watkins and Emi Buendia both scored for Villa as they signed off on a winning note ahead of their opening fixture against Newcastle United at Villa Park on Saturday.
Elsewhere, Crystal Palace have lost their UEFA appeal against being demoted from the Europa League and will play in the Conference League.
That means Villa's home match (which is scheduled for Friday, August 29) against Palace is likely to be rescheduled to Sunday, August 31.