Slomka, who signed a contract to June 30, 2016 that would also be valid if Hamburg were relegated, helped Hanover avoid relegation when he took over there in 2010. He was sacked from the club two months ago.
"There's a lot of quality in this team and it's been well put together," Slomka, 46, told a news conference in Hamburg. Slomka also coached Schalke from 2006 to 2008.
Hamburg, the only Bundesliga side to have remained in the top flight since the Bundesliga was established 50 years ago, suffered their a seventh successive league loss on Saturday, a 4-2 defeat at Bundesliga basement side Eintracht Braunschweig that left them second from bottom.
Former Netherlands coach van Marwijk was at Hamburg for 143 days after taking over from Thorsten Fink in September, with a deal until 2015. HSV were already struggling in 16th place.
Hamburg won three matches under van Marwijk and had three draws with eight defeats.
They also lost 5-0 to German Cup holders Bayern Munich in a quarter-final match on Wednesday.
Van Marwijk led the Netherlands to the 2010 World Cup final, where they lost to Spain.
Felix Magath was a leading candidate to replace van Marwijk earlier this week but an agreement could not be reached and he signed an 18-month contract to coach the English Premier League's bottom club Fulham on Friday.