Van Marwijk has been without a job since resigning as coach of the Netherlands national team last year after their poor Euro 2012 campaign.
The 61-year-old spent four years in charge of the Netherlands, having previously managed Feyenoord and Borussia Dortmund.
"HSV called me as soon as Fink was dismissed," Van Warwijk said.
"We then sat down during the week and I told them what I could offer.
"They told me what they wanted. The contract is a two-year one with an option for a third.
"Hamburg is a fantastic city and HSV have a great team with a great tradition and a beautiful stadium.
"I'm going to drive to Hamburg on Sunday morning."
Hamburg are yet to confirm Van Marwijk's appointment but club sporting director Oliver Kreuzer said last week that he wished to appoint Fink's replacement soon.
