British group Vodafone - the world's second-largest telecoms operator - announced the deal in June, which will help the company to fend off rivals in its most important market.
The European Commission said the deal did not raise concerns as it would not appreciably alter competition in the markets where the companies are currently active.
"The Commission's investigation confirmed that the activities of the merging parties were mainly complementary," the EU's executive said in a statement.
"While Kabel Deutschland primarily offers cable TV, fixed line telephony and Internet access services, Vodafone's core business consists of mobile telephony services," it added.
Vodafone, which this month agreed the sale of its stake in U.S. operator Verizon Wireless for $130 billion, wants to buy Kabel Deutschland to offer more television and fixed-line services in Germany, its largest European mobile market.
The British company last week said earlier this week it had secured 76.48 percent of Kabel Deutschland shares, which is above the 75 percent minimum acceptance condition it had set.
So-called "quad-play" services offering TV, broadband, mobile and fixed-line telephony have caught on rapidly in markets such as France and Spain, but the largely fragmented German cable market is still some way behind.
With consumers wanting to watch TV and video on an array of devices, cable assets have become more attractive as they can provide internet services at speeds often five times faster than competing services from traditional telecom companies.
(Reporting by Foo Yun Chee, Additional reporting by Harro Ten Wolde in Frankfurt; Editing by Martin Santa and Elaine Hardcastle)