Hamas, blacklisted as a terrorist group in the West, has endorsed a new payment mechanism involving the rival Palestinian Authority (PA) of president Mahmoud Abbas as well as the UN, Al-Emadi said in a statement.
He did not elaborate.
Israeli officials had previously said that the PA-and-UN-led mechanism could involve disbursing the Qatari aid as vouchers rather than cash, as a safeguard against Hamas diverting the money to military needs.
COGAT, the Israeli defence ministry agency for liaising with the Palestinians, declined comment on the Qatari announcement.
Emadi said the new agreement also entails full opening of border crossings with Gaza, which Israel and neighbouring Egypt keep cordoned off. There was no immediate word on when this might happen.
The hold-up in Qatari payouts had fuelled rancour in aid-dependant Gaza, which in recent days has seen increasingly violent border confrontations with Israel.
Emadi voiced hope that the resumption of payouts and a full border opening "will have a clear and positive impact on improving the living reality in Gaza Strip (and) help all parties emerge from the tense situation".
Qatar and Egypt have both promised funds to help rebuild the Palestinian territory. Having already pumped more than $1 billion into Gaza projects since 2014, Qatar pledged another $500 million in late May.