"Christoph thanked us for the collaboration and said he could not refuse the offer because of its very good sports and financial framework.
"We wish him all the best in his new job."
"My decision is not going against Cologne but in favour of new challenges," Daum said in a statement released through his lawyers.
"I have the chance to play internationally right away which for me as a coach is a major challenge and wish," Daum said.
Podolski, who will return to his home club after an unhappy three-year spell at Bayern, said Daum's departure was unexpected.
"This news comes as complete surprise," the striker said in Dubai ahead of Germany's friendly with United Arab Emirates later on Tuesday.
"But I am confident the club will find a worthy successor and I am certain that the club will meet its targets irrespective of the coach change."
