Kabel is the largest cable operator in Germany, offering phone, TV and broadband services to 8.5m households across the country.
It became the subject of a bidding war between Vodafone and rival US company Liberty Global - the firm that bought Virgin Media in the UK.
However, Vodafone prevailed and its German division now holds 76.57% of Kabel's share capital.
Buying Kabel has brought Vodafone's mobile customer base up to 32.4 million.
In September, Vodafone confirmed it had sold of its stake in US firm Verizon Wireless for $130bn to focus on its European operations.
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