The German club will contribute half of Tosic's wages, but will have no option to sign the player permanently, although the loan deal can be extended by a further year reports Goal.com Germany.
The 22-year-old has made only five substitute appearances for United since joining a year ago, and has not had the impact hoped for at Old Trafford.
However, Tosic is confident that he will adapt to life at his new club: "The tempo in England is much higher, so it will be very easy for me, to get into the German competition."
The player remains optimistic though that his time at Cologne can help him win a more prevalent role with the Red Devils.
“I believe I haven’t had my final say at Manchester United and that my performances with Cologne will be my ticket back to Old Trafford," he told Serbian newspaper Blic.
Tosic will wear the number 14 shirt, and took part in his first training session with his new teammates on Wednesday afternoon.