The 19-year-old has signed a three-year deal with an option for a further 12 months.
Thompson told the official Canaries website: “I’m extremely proud. To come to a club of Norwich City’s stature is a fantastic achievement for me. I’m really looking forward to the challenge of coming here after my loan finishes at Swindon.
“It’s a massive club with a huge fan base, there’s not a single negative thing to say about them. Hopefully they can do well this year and challenge for a Premier League place.”
Louis has featured regularly for Town this season and scored his first goal of the campaign against Brighton & Hove Albion last week.