According to the agreement, the 124 participants from Jordan, Mauritania, Kuwait and Syria will be picked up by buses from the Ela Prison in Beersheba, along with a number of detainees from Pakistan and Indonesia. They will be transferred to Jordan and from there to their countries of origin.
Two Lebanese who were injured in the raid - head of the Lebanese delegation on the sail, Hani Suleiman, and Nabil Halak – will be transferred to Jordan to continue their medical treatment.
According to the report, Lebanon agreed to take in the three, which include al-Jazeera correspondent in Lebanon, Abbas Nasser.
According to Interior Ministry's population and immigration administration, 682 of the sail's passengers have already undergone a hearing. More than half of them are Turkish nationals.
A ministry official estimated that all the passengers would leave Israel within days, unless a dramatic development occurred.
Some 380 of the detained and injured passengers who have undergone a hearing so far are Turkish citizens. Some of the Turks have also agreed to return home.
The rest of those who will be sent home are citizens of the United States, Ireland, Sweden, Germany and other countries. The detainees who have yet to identify themselves and agree to leave the country are waiting in prisons in the south.
Cabinet ministers argued on Tuesday evening that Israel should not allow the Turkish planes sent to retrieve those wounded in Monday's events, to do so.
"They were not injured during a picnic, but during a violent clash with IDF forces. They must be held for further interrogation and if need be – prosecuted," said one of the ministers.
Raanan Ben-Zur, Roni Sofer and Ilana Curiel contributed to this report