After the encounter, at the Erez Gaza border crossing, the Israeli Prime Minister refused to give a date for the much-postponed withdrawal of most Israeli troops from the West Bank city of Hebron.
However, the mere fact of the meeting suggests Israeli-Palestinian relations, strained to breaking-point since Mr Netanyahu was elected in May, may be healing rapidly.
The Israeli Prime Minister, who once swore that he would never meet "that man" Arafat, had two conversations with the Palestinian President in one day.
In the first, which was conducted by telephone, Mr Arafat apologised to the Israeli leader for insults which had been heaped on him in the Palestinian press.
A columnist in Al-Ayyam newspaper said on Tuesday that Mr Netanyahu was "more Nazi than Hitler".
The summit followed weeks of diplomacy by both sides, assisted by the Norwegian government.
Mr Netanyahu had said that he would meet Mr Arafat only when he had something firm to announce or to discuss an urgent security problem.
But yesterday's meeting involved neither. Afterwards, at a joint press conference, Mr Netanyahu said that he would respect accords signed by the previous, Labour, government and that he was ready to negotiate a final peace agreement.
He hoped, he said, to "improve the prosperity and economic conditions of the Palestinian population".
Mr Arafat said the meeting would lead to a full-scale resumption of the peace process. "There is no doubt that the path was cleared for us to negotiate on all levels and in all aspects."
There was no public sign of warmth between the two men, who failed to look at each other. None the less, Israeli television repeatedly showed film of their earlier four-second handshake, the first formal recognition of Mr Arafat as a partner in peace by a Prime Minister from the Likud party.
The two sides are said to be close to agreeing on a package of measures including redeployment in Hebron.
Mr Netanyahu refused to be drawn on this subject. He said that this and other issues would be discussed in an Israeli-Palestinian steering committee. Questioned on the same subject, Mr Arafat said: "I have nothing to add, but to state that we will continue to negotiate and to co-ordinate in all efforts, by all means."
The handover of Hebron to Palestinian civil rule and removal of Israeli troops from most of the city is the most contentious immediate issue between the two sides.
Mr Netanyahu's governing coalition of right-wing and religious parties has said that it wants to renegotiate the terms which Labour agreed; Palestinian officials said again and again that they were willing only to discuss implementation of the existing deal.
Hardline members of the Israeli governing coalition said that the meeting betrayed Likud policy, but Mr Netanyahu insisted that it was in line with his campaign pledges to replace the previous Palestinian negotiations with a tougher brand of "peace with security". Labour politicians and many Israeli civil servants will nevertheless take yesterday's summit as proof of what they had long predicted: that Mr Netanyahu would have to, in the short term, return to something like the Oslo peace process, because there was no other viable course.
Israeli officials said Mr Netanyahu had come to accept that Israel's security depends on co-operation with the Palestinian Authority (and that Mr Arafat has done a good - maybe too draconian - security job). Some form of Hebron deal, linked to wider access to Israel for Palestinian workers, may be possible in the near future.
The real problems will come in the medium or longer term, when Mr Netanyahu faces the core issues still undecided, such as the final status of the Palestinian authority, the future of Jerusalem and the final division of the West Bank between Palestinian areas and Israeli settlements.