The club was also knocked out in the first round of the German Cup by second-division side Sandhausen.
"The aim for the season is to stay away from the bottom part of the table," said Verbeek, who will be assisted by 48-year-old Raymond Libregts. "Of course I have my own ideas. But it always depends on the quality of the players. I have to get to know the team."
Interim coach Roger Prinzen, who led the side to a 1-1 draw at Eintracht Frankfurt on Saturday, is returning to Nuremberg's under-23 side.
Verbeek previously coached AZ Alkmaar for three years, leading the Dutch side to Europa League qualification in each season despite operating under financial constraints. He was fired in September after a win over league leader PSV Eindhoven, with reports suggesting his relationship with the team had broken down.
He was previously fired by Feyenoord in similar circumstances.
Nuremberg sports director Martin Bader said there had been no front-runner for the job and that he had conducted extensive interviews to find the best candidate.
"(Verbeek) is keen on the task and is coming with real heart and fire. You could feel that from the first minute," Bader said. "There are countless things in his favor."
Verbeek, the third Dutch coach in the Bundesliga after Bert van Marwijk at Hamburg and Jos Luhukay at Hertha Berlin, will take charge of his first game on Friday when Nuremberg visits Stuttgart.