The 19-year-old has signed a three-year contract with the German side after passing a medical.
Sala is the second Chelsea player sporting director Frank Arnesen has signed since moving from Stamford Bridge to Hamburg last month.
Hamburg signed England Under-21 international Michael Mancienne earlier this month.
“Jacopo is a player with a future,” Arsenen told Hamburg’s official website.
“He has played for all the Italy youth teams and has excellent technical and physical attributes.”
“It is a big chance for me to be able to play at Hamburg,” Sala said.
“I would like to continue my development as quickly as possible and to appear for Hamburg in the Bundesliga.
“That would be fantastic, because this big club is something special. Regardless of whether I was in Italy or England – Hamburg are known everywhere.”
