In a statement, the Spanish telco says Vivendi would obtain BRL11,962 million (€3,936 million) in cash and a 12% stake in its Brazilain subsidiary following its combination with GVT.
Furthermore, Vivendi would be allowed to buy an 8.3% stake in Telecom Italia from Telefónica.
The offer to Vivendi is subject to regulatory approval and will expire on September 3, unless accepted by Vivendi or extended by the bidder.
Quoted by Bloomberg, Vivendi said that although none of its units are for sale, it would study the offer.
Analysts believe it may be waiting for counter bids before making a decision.
Telefónica previously bid to buy GVT in 2009, only to miss out to Vivendi, which topped its offer of $4 billion with one of $4.18 billion.
Telefónica is keen on strengthening its presence in Brazil, while at the same time exiting the Italian market.
GVT currently has some 2.7 million fixed broadband customers in a market with still low broadband penetration rates.
There is also little convergence as yet in Brazil, though this is expected to change in the near future.