According to the report, the two companies declined to disclose terms of the deal.
In just over two years, Apple had sold 200 million songs in Europe, with about 150 million coming in the last 12 months, the report said.
Previously, Apple had teamed up with Coke's rival PepsiCo for a giveaway of 100 million songs in the US.
In Britain, Coke would distribute 70 million song codes inside packs of Coca-Cola and Diet Coke that could be redeemed for tracks at the iTunes store, where they usually sold for 79 pence ($1.47) each, the Reuters report said.
In Germany, Coke would give away some 67,000 iTunes songs and 1,500 iPod portable music players. Other European promotions would follow in the coming months, the report added.
The Coke-Apple alliance came weeks after Coke bowed out of the online music category by closing its mycokemusic service, one of the first European download stores when it launched in January 2004.
Since the launch of iTunes in Europe, the service's market share had slipped into insignificance, the report further said.