The two-time Belgium international, whose contract with the Gunners was set to run out next summer, has signed an undisclosed permanent deal.
"In Sambi, we have signed a midfielder who is equally as talented as he is experienced," said Hamburg board member for sport Stefan Kuntz.
"He’s shown his quality at the highest level over the past few years in the Premier League and in LaLiga and will help our team in build-up play as well as in transition.
"We're over the moon to be able to welcome him to HSV!"
