In a widely-expected move, Vodafone said it was doubling its own stake in Cegetel to 30% by buying a minority holding from US telecoms firm SBC.
In a stock market statement, Vodafone said it was a long-term investor in Cegetel and SFR and looked forward to continuing its successful partnership with Vivendi to develop these businesses.
French media conglomerate Vivendi Universal won the battle for Cegetel on Tuesday.
It upped its stake to 70% by buying British Telecom's stake in Cegetel for $4bn (£2.6bn).
Key European market
Vodafone had also been trying to buy out Vivendi's interest in Cegetel, but was rebuffed.
Vodafone said the changes meant Cegetel's ownership structure would be simplified and it would be entitled to appoint three directors instead of one as at present.
It said its higher stake in Cegetel would increase its holding in mobile phone operator SFR by 12 percentage points - from 31.9% to 43.9%.
Vodafone is paying 2.3bn euros (£1.5bn; $2.3bn) to acquire SBC's shares in the French firm.
As a result, it said, it expected to capture a greater proportion of SFR's income and to increase its exposure to France, a "strategically important" and "growing" market.
France has relatively few mobile phone users for a large European country, presenting opportunities for growth.
Shareholders cheer
Vodafone said its purchase of SBC's stake in Cegetel would benefit its shareholders by enhancing underlying earnings per share in the first year of ownership.
Shareholders had feared that Vodafone was ready to overpay for control of Cegetel.
Vodafone shares closed 1.75p higher at 121p on Wednesday.
Vivendi founded Cegetel five years ago, and sold stakes to BT, SBC, and German telecoms giant Mannesmann - now part of Vodafone.
A Cegetel shareholders' agreement gave Vivendi first priority in buying the firm's stock and precluded Vodafone from offering more money for BT's stake.