The British telecoms group, which bought close to a 77% stake in the German cable company in 2013 for 7.7 billion euros, offered all minority shareholders 103 euros in cash for each outstanding share.
Citi analyst Georgios Ierodiaconou said the tender offer was not a surprise and that was a reasonable price and would help to eliminate one of the potential risks to the group.
Vodafone said shareholders representing 17% of the shares had accepted the offer, which valued all remaining minority holdings in KDG at up to 2.12 billion euros.
Elliott, D.E. Shaw and UBS O'Connor have accepted the offer and agreed not to take further legal action against Vodafone, the statement added.
KDG minority shareholders had previously appealed against a 2019 decision by a Munich court that ruled Vodafone's compensation for the 2013 takeover as adequate.
Vodafone, the world's second-largest mobile operator, said its net debt would rise to 46.1 billion euros if all shares were tendered. Shares in the FTSE 100 firm were down 1% by 1210 GMT.
The group on Monday ended talks with the Saudi Telecom Company over the $2.4 billion sale of its shareholding in Vodafone Egypt, reaffirming its commitment to the country.
Vodafone is spinning out its mobile network towers to take advantage of investor appetite for infrastructure assets, which offer a long-term secured income stream. It will use the proceeds to reduce its debt.
Last month, Vodafone hiked its earnings outlook after a resilient first half, despite a hit to roaming revenue from coronavirus-led travel curbs.
($1 = 0.8173 euros)
(Reporting by Yadarisa Shabong in Bengaluru; Editing by Patrick Graham and Keith Weir)
By Yadarisa Shabong