Telefónica said it had won backing for its improved bid from Mexican billionaire Carlos Slim's group America Movil, which is the main shareholder of E-Plus' parent, the leading Dutch telecommunications firm KPN.
"With this agreement, Telefonica comes close to the objectives announced at the end of July in reference to becoming Europe's second largest operator," the Spanish group said in a statement.
If approved by regulators and shareholders in KPN and Telefónica Deutschland, the takeover would create a major player in Germany with 43 million mobile customer and combined revenues of €8.6 billion, it said.
America Movil, which holds 29.77 percent of KPN and has announced plans to take over the group, gave an "irrevocable commitment" to vote for the Telefonica bid for E-Plus in a KPN shareholders meeting to be held October 2, KPN said in a separate statement.
KPN said it would receive €5 billion in cash and a 20.5 percent stake in Telefónica Deutschland after the transaction, up from the previous offer of €5.0 billion and a 17.6-percent stake.
"On the basis of these improved terms, the total implied transaction value for E-Plus is now €8.55 billion," it said.
Carlos Slim's America Movil said in a separate statement that it "remains committed" to its plan to make an offer for KPN.
It said the value of Telefonica's E-Plus takeover offer had climbed to €8.55 billion from €8.1 billion in the original bid announced on July 23.