The former Netherlands coach has signed a two-year deal with the Bundesliga club to replace Thorsten Fink, who was sacked after the 6-2 thrashing against Borussia Dortmund.
HSV parted company with former boss Thorsten Fink following a 6-2 thrashing against Borussia Dortmund last week - a result that compounded a run of just one win in five Bundesliga matches - and confirmed the arrival of the former Netherlands boss after Saturday's loss to Werder Bremen.
"HSV called me right after the release of Thorsten Fink. We then sat together and I told the club what I can offer," van Marwijk told NOS Studio Sport. "The club have told me what they want. The contract runs for two years with the option of an extension of a year.
"Hamburg is a great city, HSV have an exceptional team with great tradition and an amazing stadium. I shall travel to Hamburg on Sunday morning."
The former Dortmund boss becomes the fourth Dutchman to become head coach of the club, following Martin Jol, Huub Stevens and Ricardo Moniz.
Van Marwijk will take charge of the side for the first time against Greuther Furth on Tuesday in the DFB Pokal.