The interior ministry's announcement will have limited practical impact, as Israelis had previously been travelling to Saudi Arabia via third countries, especially Jordan.
But Israel had never granted official approval for such travel by both Jewish and Muslim Israelis.
Interior Minister Aryeh Deri "signed for the first time an order enabling an exit permit for Israelis to Saudi Arabia", his office said.
The move, coordinated with the security and diplomatic services, approves travel to the Gulf state "for religious purposes during the Hajj and the Umrah", it said in a statement.
It said Israel would also allow its citizens to travel to Saudi Arabia "to participate in business meetings or seek investments" for trips not exceeding 90 days.
Business travellers must have "arranged their entry to Saudi Arabia and received an invitation from a governmental source", the interior ministry said.
There was no indication of a corresponding policy change from the Saudi side, but there have in recent months been gestures pointing to warming ties between Israel and Gulf states.
Hajj cost further jacks up due to Saudi fee
Earlier on Sunday, Israeli Prime Minister Benjamin Netanyahu praised Mohammed al-Issa, head of the Muslim World League based in Makkah for attending commemorations in Poland this week marking 75 years since the liberation of the Nazi death camp Auschwitz.
"This is another sign of change in the attitude of Islamic bodies and, of course, the Arab states toward the Holocaust and the Jewish people," he told reporters.
Israel has a peace deal with two Arab countries, Jordan and Egypt, but its occupation of Palestinian territory has long served as a major factor preventing similar accords with the rest of the Arab world.
Common concerns over Iran, however, are widely seen as having fostered closer ties between Israel and several Arab states, especially in the Gulf.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ