Former Mainz coach Klopp was unveiled at a press conference on Friday morning, signing a contract that runs until 2010.
He replaces Thomas Doll, who parted ways with the club earlier this week after Dortmund finished a lowly 13th in the Bundesliga - their worst finish in 20 years.
Klopp stepped down as coach of Second Division Mainz on Sunday.
"I am very pleased to be here," Klopp said. "For me it is an honour. Now I want to help the club compete again."
Klopp, 40, has brought assistant Zeljko Buvac to the club and is set to name the rest of his backroom staff next week.
Chairman Hans Joachim Watzke revealed Klopp had been the club's first choice for the job.
"We spoken only with him," Watzke said.