The former Hannover coach, who lost his job with the Lower Saxony club just after Christmas, becomes the 30th coach of the northern Germany side and was presented at a press conference on Monday.
"We had to make a quick appointment," said the club's chairman Carl-Edgar Jarchow. "I'm glad we were able to conclude these negotiations quickly.
"We're confident we can move away from 17th place with this coach and this team."
Slomka showed his pedigree in avoiding relegation with Hannover, whom he took over in 2010 in an even worse situation than Hamburg are in now.
He managed to save them from the drop on the final day of the season before guiding them to fourth place the following season, only narrowly missing out on a place in the Champions League behind Bayern Munich.
After guiding Hannover to back-to-back Europa League campaigns, he was relieved of his duties at the midway stage of the current campaign and replaced by Tayfun Korkut.
Less than two months later, he is back at the helm of a Bundesliga club.
"I'm delighted to be back and I'm looking forward to the challenge," he said. "Hamburg are a great club."
Hamburg are currently two points behind 16th-placed Freiburg and only a point above bottom-placed Eintracht Braunschweig, who they suffered a 4-2 defeat to on Saturday.
Their next challenge comes against Borussia Dortmund and Slomka is hoping to see an immediate improvement in the side's fortunes in spite of the size of that task.
"We need to put in a good performance for the sake of our fans," he said. "All that matters is keeping this club in the Bundesliga."