Dutchman Jol, 52, who signed a two-year contract, will begin duties at his new club at the beginning of July. He will replace Huub Stevens who quit last November to return to former club PSV Eindhoven.
Jol joined Spurs in 2004 - where he took the London club to fifth place in the Premier League in the 2005-06 season - and was sacked last October.
Fourth in the Bundesliga, Hamburg are chasing a Champions League place and have been without a permanent coach since Stevens left in November.
"I have a lot of self-confidence. It hasn't yet happened that I didn't manage to do what I wanted," Jol said, according to the Hamburger Abendblatt.