Italy Under-21 captain Caldirola, who led his team to the European Championship final earlier this month, played last season on loan for Italian second tier side Brescia.
"Werder Bremen is my big chance," said the 22-year-old, brought in to replace Greece international Sokratis Papastathopoulos, who joined Borussia Dortmund.
"I immediately agreed to this offer when my agent asked me if I wanted to join Werder Bremen. This club has a great tradition and I look forward to my time here."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.