The announcement came after the foreign ministers of both countries held talks in Brussels to resolve the decades-old row over Macedonia's name. Following Monday's discussions, Skopje said the negotiations were in "the final stages".
"We agree on the foundations and principles of the accord," Zaev told journalists on Wednesday.
He said more information would be disclosed after a planned phone call with his Greek counterpart Alexis Tsipras on Wednesday evening or Thursday.
"We'll only reveal all the details afterwards," Zaev said.
The dispute dates back to 1991, when Skopje declared independence from war-torn Yugoslavia.
Athens objects to its neighbour's constitutional name, Republic of Macedonia, because Greece has its own northern province called Macedonia, and fears it may imply territorial ambitions.
Greece wants the change of name to be backed with a constitutional amendment and for it to be applied on the "erga omnes" ("towards all") legal principle, meaning universal use inside and outside Macedonia.
The dispute has slowed Macedonia's hopes of joining the European Union and NATO, as Greece can veto the country's membership bids.
A number of countries including the United States and Russia have already recognised the country as "Macedonia".
Macedonia's parliament will need to ratify the deal before a referendum can be held, Zaev said, adding he expected the gap between both events to be "around a month".
"We want to give Greece sufficient time to send a letter to NATO" before a July 11-12 summit, the leader said.
Names already put forward and in discussion include "New Macedonia" and "Upper Macedonia".
"There are no secrets or unknown (factors)," Zaev said Wednesday without elaborating.
A senior Macedonian government official told AFP that "Upper Macedonia" was a favourite.
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