The Bundesliga club confirmed the arrival of the 61-year-old Dutchman on Monday, with van Marwijk signing a two-year contract.
Fink was dismissed following Hamburg's 6-2 defeat to Borussia Dortmund nine days ago after collecting just one league win this season.
Temporary boss Otto Addo oversaw a 2-0 loss at home to Werder Bremen on Saturday that leaves Hamburg in 16th place in the German top flight.
Addo will remain in charge for the DFB-Pokal clash with Greuther Furth on Tuesday, meaning Van Marwijk's first game in the dugout will be Saturday's match at Eintracht Frankfurt.
Sporting director Oliver Kreuzer welcomed the Dutchman to the club and backed him to turn their fortunes around.
"We are pleased that we were able to appoint Bert van Marwijk as coach of HSV," he told Hamburg's official website.
"He has extensive experience and has proven his competence in numerous cases."
Van Marwijk's last job was as the Netherlands national team manager between 2008 and 2012, a spell during which he took his country to the 2010 FIFA World Cup final.
He was relieved of his duties after they were eliminated from last year's UEFA European Championships with zero points from their three group games.
This will be his second job in the Bundesliga, after he managed Dortmund for two years from 2004.
