Norwegian Solbakken, yet to take charge of a competitive match since joining the club in June, acknowledged the decision could stir up discontent less than two weeks before the start of the Bundesliga season.
"I can understand the reactions this decision will provoke and I can understand the disappointment of some fans," the coach told reporters.
"But I ask the fans to understand my decision is for the benefit of the whole team. Pedro Geromel will as captain exemplify the new culture of the team and embody our new overall sporting concept," Solbakken added.
"In my conversations with him, Lukas has expressed his disappointment but at the same time respected and understood the reasons for my decision."
Podolski, 26, returned to Cologne in 2009 after three seasons of mixed fortunes with Bayern Munich and is a favourite of the supporters.
He scored 13 Bundesliga goals last season to help the club finish 10th. He has been a regular for Germany since 2004, making 89 appearances.
Geromel joined Cologne in 2008 from Vitoria Guimaraes of Portugal.
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