Basel boss Fink joins troubled Hamburg
The decision ends weeks of speculation regarding Fink, who had a contract at Basel until 2013, and is expected to ease the tension at the former European champions, who have won only once this season and sit bottom of the 18-team table.
"Fink was top of my wish list," Hamburg sporting director Frank Arnesen said in a statement. "He will improve our team and develop it further."
Prior to joining Basel in 2009, Fink, who had played for Bayern Munich, had coached Austria's Red Bull Salzburg and Ingolstadt 04, whom he led to the second division in Germany.
Hamburg have been without a coach since the sacking of Michael Oenning last month with interim coach Rodolfo Cardoso's provisional licence to lead a Bundesliga club having expired after two league games in charge.
Arnesen will coach the team for Sunday's match at Freiburg before Fink's official presentation next week.
Hamburg are the only club to have never been relegated from the Bundesliga.