"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".
Both governments have faced criticism ahead of the compromise and on Tuesday Macedonia's President Gjorge Ivanov signalled his concern.
Significantly, they agreed that the new name would be used both internationally and bilaterally, so that even the 140 or more countries that recognize the name Macedonia will also have to adopt North Macedonia.
The prime ministers of Greece and Macedonia say they have agreed on "Republic of Northern Macedonia" as the new name for the Balkan country, ending a bitter 27-year dispute that had prevented the former Yugoslav republic from joining global institutions such as North Atlantic Treaty Organisation.
The "new" Slavic people calling themselves Macedonians did not help matters when they named the main airport in the capital, Skopje, after Ancient Greek hero Alexander the Great, as well as a key highway running from Skopje to the Greek border.
Athens has long objected to its neighbour's constitutional name - the Republic of Macedonia - because it fears it could imply territorial ambitions.
The name dispute has poisoned relations between the two countries since Macedonia's independence from Yugoslavia in 1991 and has prevented Macedonia from joining worldwide institutions such as North Atlantic Treaty Organisation and the European Union.
Skopje hopes that with a solution in hand, North Atlantic Treaty Organisation will extend an invitation to join and the European Union will allow the start of Macedonian accession talks as early as this summer.
European Council President Donald Tusk tweeted his support for the agreement: "Thanks to you the impossible is becoming possible".
"We got a fair deal..."
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".
The Greek government has spent 27 years fighting with Macedonia over the use of the name, which references ancient Macedonia and by association its famous leader, Alexander the Great.
He said that the accord would allow a clear distinction between Greece's Macedonia province and the country.
The row between Athens and Skopje has been ongoing since 1991, when Macedonia seceded from Yugoslavia and declared its independence.
Because of Greek objections, Macedonia was admitted to the United Nations under a provisional name, the Former Yugoslav Republic of Macedonia.
Following the latest round of discussions, Macedonia is now set to be known as the Republic of Northern Macedonia. Greek opponents of the deal say modifying the name would not go far enough.
But Greek Defense Minister Panos Kammenos, whose right-wing Independent Greeks party is Tsipras' junior coalition partner, said he would reject the name agreement in a parliamentary vote.