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The 20-year-old had previously been on the books of fellow top-flight side Tottenham, but his contract at White Hart Lane expired.
Gallifuoco has now moved to the Liberty Stadium and will play predominantly in the club's Under-21 squad.
"I'm very excited," he told the club's official website. "It's the perfect club for me to take the next step in my career and I can't wait to get started.
"I had a brief chat with [manager] Garry Monk and he said that there are opportunities at this club if I work hard and that's what I intend to do.
"I was excited when I learned of the club's interest and it's a Premier League club that plays brilliant football and I'm delighted to be here."
Swansea have beaten Manchester United and Burnley in the top flight so far this season and will attempt for a hat-trick of wins at home to West Brom on Saturday.
