Caldirola, 22, who is the captain of the Italian Under-21 side, passed a medical and put pen to paper on a four-year contract at the Weserstadion on Wednesday.
"Bremen is a great opportunity for me," he told his new club's official website.
"When my agent told me about the interest of the club I immediately said that I would love to play in Bremen. It is a club of great tradition and I cannot wait to start."
Caldirola was named in UEFA's Team of the Tournament following this summer's European Under-21 Championship in Israel.