"We stand on the verge of framework for a deal... resolving issues going back many decades," Tsipras said late Tuesday after a meeting with Archbishop Ieronymos, head of the Orthodox Church of Greece.
The agreement is to end the long-running designation of clerics as civil servants, in theory freeing up some 10,000 jobs on the state payroll.
The state will continue to pay church salaries under a different account, but under the proposed deal it stands to acquire an equal share in valuable church lands whose ownership has been a matter of dispute since the 1950s.
A joint state-church fund will also be created to develop this property, whose full value is still being evaluated.
After the announcement drew criticism from some senior Greek clerics on Wednesday, Ieronymos said that the proposals would not be applied without the consent of the church hierarchy.
Tsipras' political opponents have lambasted the suggestion that 10,000 state jobs will be freed up, at a time when his party is struggling in opinion polls a year before national elections.
The move also comes ahead of a Tsipras initiative to overhaul the Greek constitution.
Government plans to revise the constitution's Article 3, which states that Orthodoxy is the country's "dominant" religion -- to the consternation of rights groups -- have unnerved church circles.
A leftist and self-avowed atheist, Tsipras had announced his intention in 2016 to make the Greek state "religion-neutral".
One of the most powerful institutions in the country with influence in politics and justice, the Orthodox Church lays claim to extensive holdings around the country, many of which cannot be developed owing to court disputes.
Church officials have consistently bemoaned the level of tax levied on clerical real estate, pointing to church donations in the 19th century for the creation of schools, public squares and other state infrastructure during the early history of the modern Greek state.
Earlier this week a Greek monastery lost a court case in which it argued that church property on lease should be exempted from land tax.
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