The Cameroon international has signed on loan until the end of the season in a deal worth around £650,000 to The Hammers, who signed him from Liverpool in a £2.5 million deal a year ago.
However, Song has the option of making a permanent switch to the Mungersdorfer Stadion with a three-year deal on the table should both parties feel the move has been a success.
Hammers managing director Paul Aldridge said: "It is very important for Rigobert that he plays for his country in the World Cup finals next summer, and to this end we have let him go where he can get regular first team football.
"We wish him all the best and, as with all our players when they go out on loan, we will keep a close eye and in constant contact with him."
Cologne have been looking to increase their defensive options and Song could even make his debut in the clash with St Pauli on Saturday.
The 25-year-old Olympic Games gold medalist trained with his new team-mates on Friday and will be looking to help them end a run of seven straight defeats.
