Details of the terms of the agreement remained sketchy, but according to reports on Italian television the deal was finally struck in Milan after objections of a minority of Telecom Italia board members were overcome.
It is understood that the Telecom Italia board approval is conditional on the German government guaranteeing parity between the two companies in the enlarged group.
Earlier in the day it had seemed that the deal - the biggest merger in European corporate history - was slipping away because of Italian concerns about the shareholding structure.
The merger as initially proposed would have left Deutsche Telekom with 56 per cent of the enlarged company and effective management control. Under the provisional terms, Telecom Italia shares would have been valued at 12.72 euros, valuing the company overall at $67bn against Deutsche Telekom's market value of $110bn.
But Telecom Italia board members were holding out for a merger agreement that would give each company equal stakes of 50 per cent, despite the fact that the German company is considerably larger. The Telecom Italia board is now expected to meet today to convene a shareholders meeting to approve the merger provided it received a German guarantee of parity.
If the deal goes through, it will thwart a rival hostile offer from Olivetti, valuing Telecom Italia at 11.5 euros a share or pounds 40bn. Olivetti increased its bid from 10 euros earlier this month.
Meanwhile, the French accused Deutsche Telekom of stabbing them in the back over the merger and have warned that the Germans could face financial sanctions if they press ahead with the deal.
France Telecom, which says the deal would be a breach of the cross-shareholding agreement the French and German telephone companies signed last autumn, said in a statement: "The agreements with Deutsche Telekom are precise and incompatible with a unilateral strategic change of direction."
France Telecom is outraged that the deal has been negotiated, as it sees it, behind its back. Sources say that the first the France Telecom chairman, Michel Bon, heard of the talks was on Monday when he attended a Deutsche Telekom board meeting in Bonn.
France Telecom shares have been badly hit in Paris, falling more than 5 per cent on Monday alone. Analysts in France are already pronouncing the France Telecom-Deutsche Telekom deal dead, saying the attempts by the two to work jointly to break into the UK and Italian markets were moribund.Reuse content