Macedonia has agreed to change its name to Northern Macedonia in order to end a decades-old row with Greece, which among other things prevented the former Yugoslav republic from joining the European Union and North Atlantic Treaty Organisation.
On the timeline of the deal, Tsipras said that it would be first signed by the two countries' foreign ministers and then ratified by Macedonia's parliament.
Following the latest round of discussions, Macedonia is now set to be known as the Republic of Northern Macedonia.
The nationality of the country's citizens will be listed on official documents as "Macedonian/citizen of the Republic of Macedonia".
The neighboring nations Greece and Macedonia have been debating Macedonia's chosen name since 1991, when the small country that was once part of the former Yugoslavia adopted the name.
Due to the name dispute, Greece has vetoed all of attempts by Skopje to join both the European Union and North Atlantic Treaty Organisation.
Greece regards "Macedonia" as a term referring only to one of its northern regions and the ancient Kingdom of Macedonia, and insists on the use of another name for its northern neighbor.
Macedonia had proposed four names to resolve the dispute: Republic of North Macedonia, Republic of Upper Macedonia, Republic of Vardar Macedonia and Republic of Macedonia (Skopje).
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"We have been solving a two-and-a-half decade dispute ... that has been drowning the country", he said, adding that the deal "will strengthen the Macedonian identity".
NATO Secretary General Jens Stoltenberg said Tuesday's "historic agreement" was "testament to many years of patient diplomacy", and called on the two countries' prime ministers to finalize the deal. Macedonia is the birthplace of Alexander the Great.
The two nations settled on a name- certain to incite controversy amongst many Greeks both inside the country, as well as outside her borders.
However, Mr Tsipras said, this will be contingent on Macedonia completing the constitutional changes. But the new deal will also emphasize the fact that Macedonians to the north speak a Slavic language and don't have a linguistic kinship with the Macedonians of Greece. "I am keeping my fingers crossed".
Both governments have faced criticism ahead of the compromise and on Tuesday Macedonia's President Gjorge Ivanov signalled his concern. So if you like The Pappas Post and want to help, please consider becoming a "philotimo subscriber". Greek opponents of the deal say modifying the name would not go far enough.
A bronze statue of Alexander the Great can be seen in the northern port city of Thessaloniki, Greece.
Greek Defence Minister Panos Kammenos, a hardline junior coalition partner in Tsipras's government, earlier dismissed talk of a deal, saying there was "no chance" Zaev could get it approved.
European Union foreign affairs chief Federica Mogherini and commissioner Johannes Hahn issued a joint statement congratulating the two prime ministers "in reaching this historic agreement between their countries, which contributes to the transformation of the entire region of southeast Europe".