The 24-year-old joins from German second-tier side 1860 Munich for an undisclosed fee, and pens a three-year deal at the RheinEnergieStadion.
Osako had only been in Munich since January after he completed the switch from Kashima Antlers in his homeland.
He scored six goals in 15 matches during his brief spell at the Allianz Arena, and did enough to convince Cologne to take a gamble on his services in the top flight.
Currently, Osako is in Florida where he is preparing for the upcoming FIFA World Cup in Brazil, and he was happy to sort his future before the tournament started.
"It's a relief to get the move before the World Cup," he said. "For me the Bundesliga is one of the best in the world and I'm sure I can keep improving in Germany.
"It's given me something else to look forward to before the World Cup.
"But first I have to give everything for Japan and hopefully take some good form to my new team."
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