Predecessor Bert van Marwijk was dismissed following the club's 4-2 league reverse to Eintracht Braunschweig on Saturday - their eighth consecutive defeat in all competitions.
That loss to bottom side Braunschweig left Hamburg just a point off the foot of the Bundesliga table and three adrift of safety.
And the club confirmed on Monday that Slomka, who was sacked by Hannover earlier this season, has taken over at the Imtech Arena, becoming their eighth permanent manager in the last seven years.
Slomka managed Schalke to a second-place finish in the Bundesliga in 2007, before leading Hannover to a club-record fourth spot four years later.
The 46-year-old left the HDI-Arena in December after three years in charge, and his first match as Hamburg coach comes against third-placed Borussia Dortmund on Saturday.
The seven-time German champions have never been relegated from the top flight - a record Slomka is determined to preserve.
"I am looking forward to the challenge and will devote all my energy into keeping the team in the division," he commented.
Hamburg sporting director Oliver Kreuzer added: "It was important for us to find someone who has already experienced such a situation and has positive experience with them."
