"We have a good agreement that covers all the preconditions the Greek side had set", he said, adding that Macedonia would revise its Constitution for the name change and that the deal "secures the historic heritage of ancient Greek Macedonia".
Zoran Zaev, the prime minister of Macedonia, and Alexis Tsipras, the prime minister of Greece, both agreed to the deal on Monday.
Macedonia, the name of the ex-Yugoslav republic since its independence in 1991, has poisoned relations between Athens and Skopje for almost three decades.
"In essence, the (deal) is acceptance of all Greek positions", VMRO-DPMNE leader Hristijan Mickoski said.
"Macedonia will be called the Republic of Northern Macedonia [Severna Makedonija]", Zoran Zaev, the country's prime minister, announced Tuesday. A meeting of the two soon may seal the deal, he said.
If the name change is approved by the Macedonian people and the parliaments of both nations, then it would pave the way for the tiny Balkan nation's eventual North Atlantic Treaty Organisation and European Union memberships.
Athens and Skopje had been racing to agree the outline of a settlement before an European Union summit in late June, though any accord would need to clear a referendum in Macedonia and win approval from politicians in both countries.
The current prime ministers' attempts to end the dispute have faced dissent in both countries, leading to large protests by opponents of a compromise, threatening to split Greece's governing coalition and provoking a rift between Macedonia's prime minister and president. He added that Macedonia "cannot and will not be able in the future to claim any connection with the ancient Greek civilization of Macedonia".
Greek media previously reported today that Zaev is going to talk with Tsipras and confirm the agreement that they accomplished earlier today.
Speaking at a news conference in the Macedonian capital, Skopje, Zaev described the deal as a "historic agreement of the century". "We want to be part of a solution", said an official at the opposition Socialist Party. A North Atlantic Treaty Organisation summit is scheduled for mid-July.
"This historic agreement is testament to many years of patient diplomacy, and to the willingness of these two leaders to solve a dispute which has affected the region for too long", said NATO Secretary General Jens Stoltenberg in a statement.
Athens, which like all members of both organisations has a veto over admissions, objected to its neighbour's use of the name Macedonia, arguing that it, along with articles in the constitution, could imply territorial claims over its own northern region of the same name.
The United Nations envoy who mediated the dispute for two decades congratulated Tsipras and Zaev for resolving their differences.