Under the agreement, Vodafone will pay €4bn (£2.5bn) for BT's 26% stake and €2.3bn (£1.5bn) for SBC's 15% stake.
Vodafone has also made a non-binding cash offer of €6.7bn (£4.3bn) to Vivendi Universal to sell its 44% stake in Cegetel.
Vivendi has the right to pre-empt either or both of the BT and SBC interests until 10 November by buying them itself. To do so, Vivendi would have to pay cash on the same terms as Vodafone for the BT stake and at a 13% premium for the SBC stake.
By acquiring the BT and SBC stakes, Vodafone will increase its influence in Société Française du Radiotéléphone (SFR), France's second-largest mobile phone company and Cegetel's crown jewel. Cegetel owns 80% of SFR, and Vodafone the rest.
France is the only major wireless market in Europe in which Vodafone lacks control of a local operator. In all other key markets - the UK, Germany, Italy and Spain - Vodafone either fully owns or has a majority stake in a domestic mobile phone operator.
Vodafone is particularly keen to tap the French market, which is relatively underdeveloped compared with the other big markets.