"Vodafone announces that the 75 percent minimum acceptance condition has been met," the British company said in a statement.
As a pre-requisite of the deal, proposed in July, Vodafone needed to secure at least 75 percent of shares to succeed.
Vodafone added it would publish the final proportion of shares offered on September 16.
Kabel Deutschland also confirmed the shareholders' decision in a statement issued Thursday.
The deal still needs to receive regulatory approval from the European Commission, which is due to complete a first review on September 20.
Shareholders who have not yet tendered their shares now have an additional two weeks, between September 17 and 30, to do so. Vodafone is offering them 87 euros per share.
The offer is supported by Kabel Deutschland's management and supervisory boards, but its success was in doubt earlier this week given the high threshold for success.
With 8.5 million subscribers and 1.7 billion euros of annual turnover, Kabel Deutschland is the largest cable operator in Germany.
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.
Vodafone is flush with cash after selling off its stake in a US joint venture to partners Verizon for $130 billion earlier this month.