He joined Villa in 2020 and scored in their FA Cup third round tie against Liverpool last January.
He spent the half of the season on loan at Ipswich, making six appearances.
"Louie comes to us with undoubted ability," said Swindon director of football Ben Chorley.
"He has been on the biggest of stages for such a young man. Over the last three weeks we've watched every minute of his games live and been in constant dialogue with his club."
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