The agreement will see the PA give Israel a reciprocal number of doses from one of its own shipments due to arrive later this year.
The Pfizer-BioNTech jabs to be handed over are close to their expiry date.
Israel has faced criticism that it has not done enough to help vaccination efforts in the occupied territories.
About 55% of eligible Israelis have been given both doses as part of a mass vaccination campaign after the country obtained millions of doses of the Pfizer-BioNTech vaccine.
Some 30% of eligible Palestinians in the occupied West Bank and Gaza have received at least one vaccine dose, according to Palestinian officials.
The deal involving between 1.0-1.4 million doses was announced by the office of the new Israeli Prime Minister Naftali Bennett, who was sworn in on Sunday, replacing Benjamin Netanyahu.
It was not yet clear when the doses would be sent to the Palestinians. A statement from the Israeli government said Israel expected to receive reciprocal doses from the Pfizer shipment to the PA in September or October.
from Russia, China, the United Arab Emirates and the global Covax vaccine-sharing initiative.
UN experts had been critical of Israel’s failure to fully extend its vaccination programme to Palestinians under its control. The country reached a special deal with Pfizer, in which it provided vital medical data in return for a quick rollout of the vaccine.
The Israelis said the Palestinians were responsible for managing health matters in the territories.