"We think we've got a bit of clarity from this decision because some things were confusing." Cologne chairman Werner Wolf told Focus magazine on Sunday.
"There have been several discussions between representatives of Cologne's shareholders and Volker Fink about selections on the field," said Wolf just hours after Cologne's win against Hertha Berlin on Saturday.
"Due to differences of opinion, both sides have agreed to separate with immediate effect," he said.
Cologne's Norwegian coach Stale Solbakken led his team to their first win in five games against Hertha which left his team 13th in the league.
Pressure had mounted on Finke this week as the club struggled to keep hold of star forward Lukas Podolski.
Reports in both the German and British media last week said Podolski is set to join Premier league side Arsenal at the end of the season, although the 26-year-old insisted the deal is far from done.
Podolski received a straight red on 76 minutes after a clash with Hertha defender Levan Kobiashvili.