In a statement, the Commission, the Europan Union's executive, said an "investigation confirmed that the activities of the merging parties were mainly complementary" and would not "appreciably alter competition".
With 8.5 million subscribers and €1.7 billion of annual turnover, Kabel Deutschland is the largest cable operator in Germany.
Vodafone is flush with cash after selling off its stake in a US joint venture to partners Verizon for $130 billion earlier this month.
On September 13th, shareholders of Kabel Deutschland gave the go-ahead for the acquisition priced at 87 euros per share.
The deal comes during a period of consolidation within the European cable industry.
Liberty Global announced in February the acquisition of its British rival Virgin Media in a deal worth $23.3 billion.