The deal breaks down to an offer of $104.70 per Kabel Deutschland share, The New York Times reported. That includes a $3.27 dividend the German firm had committed to in February, the Times said.
The offer represents a 40 percent premium over the German company's market value in February, when news of a potential deal reached the public.
"Kabel Deutschland and Vodafone are an ideal fit," said Kabel Deutschland Chief Executive Officer Adrian von Hammerstein in a statement.
For Vodafone, the deal adds to its position in Germany, which is substantial. In 2000, Vodafone purchased Mannesmann, a German wireless provider, for $183 billion.
The Times said the expanded Vodafone would have 32 million telephone customers and 5 million broadband users. In addition, the firm is acquiring a business with 8 million cable subscribers in Germany.
"The combination of Vodafone Germany and Kabel Deutschland will greatly enhance our offerings," Vodafone's chief executive, Vittorio Colao, said in a statement.