Details of the coalition -- especially those about which parties will actually contribute members to the cabinet -- are expected to be revealed later Wednesday, the BBC reported.
Greek Socialists (Pasok) chief Evangelos Venizelos made the announcement following his meeting with Antonis Samaras, head of New Democracy, who had earlier in the day hammered out a deal with Democratic Left party chief Fotis Kouvelis.
The coalition represents a majority of 179 out of 300 seats in Parliament. Syriza, which is is radically against the bailout and holds 71 seats, would likely have had the support of the Communists, who hold 12 seats.
The formation of the coalition is necessary before Greece can start the process of receiving $130 billion in bailout funds from the European Union and the International Monetary Fund.
While the leftists have pledged support for a government, they remain uncommitted to placing members in the cabinet.
The leaders have decided in principle to support this coalition. What we are discussing now is who will participate in it, a member of the inter-party negotiating committee told Reuters.
Whatever shape the new government will take when it is formed, it will need to confront highly unpopular austerity measures, which are required to receive assistance, including contributions from IMF member countries.
The fate of Greece has been in flux since it failed to emerge from May 6 elections with a functioning government. In Sunday's parliamentary election, New Democracy gained 21 seats while the Pasok and Democratic Left parties lost ground.
Pasok chief Evangelos Venizelos is adamant that the socialists must not participate in a Cabinet that would back harsh austerity measures.
Meanwhile, German officials are calling for more decisiveness and want to see a faster pace in the implementation of bailout requirements, although the EU has given indications it would make some concessions.
In recent days, international companies have been divesting their Greek branches, according to a report by the New York Times. French supermarket giant Carrefour SA (Paris: CA) sold its Greek branch to its local partner at a loss, Coca Cola's Greek operations were downgraded by Moody's Investors Service, and various import-export insurance companies have stopped covering transactions with Greek companies.
In addition, Greece risks blackouts as Russian gas giant Gazprom has said it will cut the country off if it does not pay its bills by June 22.
The only things that have been selling well recently have been staple foods like pasta and canned goods, which have been flying off the shelves. Greeks are stocking up on non-perishable food in panic-buying mode as they prepare for shadowy worst-case-scenarios following the election. A quiet rush on banks has been occurring, with $1 billion in deposits leaving Greek banks each day for some time.