NBG said in a statement that the proposal called for Eurobank shareholders to receive 58 new shares for every 100 that they own. Eurobank CEO Nikolaos Nanopoulos said his bank's board would examine the proposal "in a constructive spirit."
Greek banks are under pressure to merge after experiencing severe damage from the three-year-old financial crisis and a major write-down in the country's debt earlier this year.
"Today's public offer aims to create a broader banking group in Greece that will ... stabilize the Greek banking system and provide the necessary financing to support Greece's economic recovery," NBG chairman George Zannias said in a statement.
NBG said that together, the two lenders would have deposits of €87.9 billion ($114.3 billion), loans of €109.7 billion ($142.6 billion) and a network of 925 branches in Greece.
Earlier Friday, Greek stock market authorities temporarily suspended trading in the two banks following media reports that a merger was possible.
Anticipation of a deal fuelled a strong rally on the Athens stock market, with the benchmark general share index closing 5.05 per cent up. The bank sector posted gains of nearly 10 per cent.
Shortly before the decision, NBG and Eurobank shares were up 4.5 and 5.5 per cent, respectively.