The Italy U21 international follows Blues pal Michael Mancienne in signing for the Germans.
Sala said: "It is a big chance for me to be able to play at Hamburg. 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."
The Italian could soon be joined in northern Germany by fellow teenager Bruma.
"Jeffrey Bruma is on duty with Holland," Hamburg chief Frank Arnesen said.
"Afterwards, we will meet and talk about it. We will look each other straight in the eye. We will decide what is best for Jeffrey Bruma and Hamburg."