Kabel Deutschland is Germany's leading cable provider, providing television, telephony and broadband services to about 8.5 million connected households in 13 of Germany's 16 federal states.
(Also see: Vodafone may trump Liberty with $10 billion cash bid for Kabel Deutschland - sources)
Vodafone said in a statement it would offer Kabel Deutschland shareholders 87 euros in cash for every share.
The offer included the purchase price of 84.50 euros per share plus the 2.50 euro dividend announced by Kabel Deutschland in February.
Kabel Deutschland shares had closed at 84.10 euros on Friday.
The management and supervisory boards of Kabel Deutschland "welcome the transaction, (and) intend to recommend Kabel Deutschland shareholders accept the offer," Vodafone said.
Kabel Deutschland would provide Vodafone "with an attractive platform for TV and fixed broadband in Germany and creates a leading integrated operator with pro forma revenues of approximately 11.5 billion euros," the statement said.
Vodafone's bid comes amid rising interest in cable assets Europe.
Last week, Kabel Deutschland confirmed it had been approached about a potential tie-up by Liberty Global.
Liberty acquired another German cable operator, Kabel Baden-Wuerttemberg, two years ago.
In London, Vodafone shares were outperforming the overall market, adding 1.18 percent, while the FTSE index was up only 0.25 percent.
In Frankfurt, Kabel Deutschland shares added 1.70 percent to 85.53 euros.
For the latest tech news and reviews, follow Gadgets 360 on X, Facebook, WhatsApp, Threads and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel. If you want to know everything about top influencers, follow our in-house Who'sThat360 on Instagram and YouTube.