Greek objections delayed United Nations recognition of Macedonia until April 1993, and then only as The Former Yugoslav Republic of Macedonia (FYROM).
The delegations will sign the agreement on the Greek side of the border before crossing over to the Macedonian side for lunch, Athens said.
Macedonia's parliament will still need to approve the deal, with a referendum to follow in September or October.
Macedonia's Prime Minister Zaev said the deal put an end of the barren policies of the past that focused on isolation and self-isolation.
But from the moment the details emerged, a political storm erupted in both countries.
Tsipras and Zaev last week beat the odds to announce a deal that will see the tiny Balkan state renamed as the Republic of North Macedonia.
Thousands of Greeks protested outside Parliament against the accord with Macedonia, waving Greek flags and chanting anti-government slogans, calling for Mr Tsipras to resign.
"Recalling his first meeting with Zaev earlier this year at the World Economic Forum in Davos, Switzerland, Tsipras told Zaev that "'very few believed we would succeed" in ending what he called "26 years of sterile dispute between our countries".
One member of parliament from the Neo Nazi Golden Dawn party was removed during deliberations when he called on Greece's military to intervene and hold Tsipras before a firing squad for treason. On June 17 Macedonia's main opposition party VMRO-DPMNE is staging a huge protest in the city of Bitola against the signing of the deal. The document, in which Greece agrees to drop its veto over Macedonia's European Union and North Atlantic Treaty Organisation membership, and will be submitted to the parliament in Skopje Tuesday. There is a Macedonian minority in northern Greece which is nearly totally assimilated after Greece gained the territory following the Second Balkan War, with the people there having no right to declare themselves as Macedonians by ethnicity or to speak the Macedonian language.
Athens had long objected to it being called Macedonia because it has its own northern province of the same name, which in ancient times was the cradle of Alexander the Great's empire - a source of intense pride to modern-day Greeks.
Ahead of the no-confidence vote, senior opposition lawmaker Fofi Gennimata said the deal needed to be "improved before it is too late".
Senior EU officials were also present at the signing ceremony. Macedonian President Gjorge Ivanov said he would use his veto to block the deal, according to media reports.
The president of Macedonia has said he will not endorse the pact, while in Greece, Tsipras's right-wing coalition partners have said their lawmakers will reject it when it is brought for ratification.
In Greece, the deal faces ratification in parliament only after Macedonia has completed its part of the process.