He will be released on Wednesday after it emerged that there had been an error about his identity.
The arrested man shares the same name as an Irish “terrorist," said an Israeli official in Jerusalem on condition of anonymity.
"The Irishman whom we arrested has cooperated fully with inquiries and given all the necessary explanations about his activities in Israel and in Judea and Samaria (the West Bank)," the official said.
But the official added that the man was likely to be told to leave the country as he had been carrying out "political activities" after having entered Israel on a tourist visa.
Israeli forces said they arrested John Morgan, 40 on Saturday on suspicion of being a member of the Real IRA, a faction that has rejected the main IRA's truce with the British government.
He was detained by Israeli border guards south of Ramallah in the West Bank, near a checkpoint north of Jerusalem.
Fears that Israeli security services may have arrested the wrong man rather than a former member of the Irish Republican Army (IRA) emerged on Monday when a pro-Palestinian rights group insisted there had been a case of mistaken identity.
"We very much believe that the Israeli authorities have got the wrong person," said Kathleen Connell, spokeswoman for the Ireland Palestine Solidarity Campaign in the Northern Ireland capital Belfast.
Connell said Sean O'Muireagain was a member of her rights group. John Morgan is the English-language translation of the Irish name Sean O'Muireagain.