The former Basel midfielder arrives at the Imtech Arena days after Ivica Olic agreed a return to the club, but they remain in 16th place in the league table.
With Hamburg struggling for a second successive Bundesliga campaign, head coach Joe Zinnbauer will be hopeful the Chile international can help move them away from danger in the second half of the season.
Diaz is confident his new side have enough to climb the table, and is looking forward to a potential debut against Paderborn on Wednesday.
"I am very happy to be here and will help keep us in the division," he said. "I am sure that we will get there."
During his time in Switzerland, Diaz scored 13 goals in all competitions as he helped them win two league titles and book a place in the UEFA Champions League knockout stages this season.
