The Brotherhood has won, and its man has reached the presidential office in Cairo - although he has "limited, redefined responsibilities" thanks to the still-ruling military council - as the first freely elected Egyptian president.

This is not only the official ending of Hosni Mubarak's regime but also the beginning of a New Arab Order.

So what should the Arabs expect from Mohammed Morsi?

Until recently it appeared that the Muslim Brotherhood did not want to provoke anyone, at home or abroad.

The leaders in the new government are well aware that getting off to a good start with the public depends on the number of jobs they create, and on law and order, more than on an immediate showdown with the generals or a sweeping foreign-policy change.

Restoring law and order is obviously the Egyptian street's priority. Ahmed Shafiq's emphasis on this point in the campaign partly explains his strong showing; the law-and-order line was applauded in Egypt and in neighbouring countries, and welcomed by investors and tourists.

That may not be Mr Morsi's priority, however. The presidential decree that led to yesterday's brief, limited session of Parliament, suggests that the Brotherhood is prepared to push the generals.

Still, if the immediate constitutional crisis is defused, the new president could well delay a showdown over the armed forces' prerogatives, possibly following Turkey's example on this. It took a decade for Turkish civilian leaders to transform the military from kingmakers to partners and then to simply a national army.

In Egypt, the process could begin with Field Marshal Hussein Tantawi stepping down within the next few weeks, at a ceremony attended by the new president and key administration figures.

As he prepares to visit Saudi Arabia, then, Mr Morsi leaves considerable tension at home. This will increase his need for stability in dealing with Egypt's neighbours.

Mr Morsi knows that Arabs want Egypt to resume its "national" - meaning pan-Arab - role in the Middle East. Failure in that task was one of the criticisms of the Mubarak regime. The country's new leader needs to be able to speak abroad for Egypt, not merely for the Brotherhood. So there will be no talk of "caliphate" or Islamic unity, no promises of liberating Palestine, no big celebration involving fellow Islamists.

The Brotherhood knows how many factions and groups are apprehensive about its rise, and will be cautious about rash remarks and hasty actions.

Today, the prevailing discourse in Arab foreign policy circles and in Arab League corridors is Pan-Arabist, and far from Islamist.

You can imagine the reaction in such circles if a new Egyptian foreign minister spoke, for instance, of "virtuous succession."

Despite the parliamentary crisis at home, the president is set to land in Saudi Arabia today. The visit should be warmly welcomed in Riyadh, with the Saudis seizing the occasion to reiterate their strategic links to Egypt.

The two countries need each other, and several issues are awaiting their joint handling, including Palestinian reconciliation, Iran, Iraq and partnership with Turkey.

As much as it welcomes the Turks' return to the Arab world as a friend, Saudi Arabia is concerned by Ankara's economic expansionism and its perception of the region solely as an investment field. A Saudi-Egyptian partnership would redress this anomaly.

Then there's Syria, where the Arab world yearns for Egypt to play a constructive, even decisive role. Bashar Al Assad's regime seems unlikely to collapse in the next few weeks or months. Saudi Arabia wants the massacres to end. So does Turkey. Now Egypt has an opportunity to resume its responsibilities through actions and not simply fiery speeches.

Tackling Syria could be a boon for Egypt and its new administration. Bringing down that sectarian regime would return Syria to the Arab and regional fold, of which Egypt is the mainstay.

Such a return will open the door to significant economic integration projects, liable to change the face of the region by bringing together its four key players: Egypt, Saudi Arabia, Syria and Turkey.

Next on the new Egyptian president's itinerary should be the UAE, if only to allay its concerns over the Muslim Brotherhood's ascendancy. Mr Morsi need not make gratuitous non-interference pledges there or anywhere; indeed repeated denials are construed as evidence to the contrary. In Abu Dhabi, he would need only to reiterate his commitment to excellent bilateral ties.

As for Gaza, an early visit there by Mr Morsi could antagonise Israel prematurely. Easing the siege on Gaza and promoting Palestinian reconciliation would do, for now.

Then there is Turkey. When he goes there, Mr Morsi should take a sizeable trade delegation, as Mr Erdogan usually does on his travels. The president can then move on to Sudan, the other economic partner of the new Egypt.

A final thought: Will the Muslim Brotherhood break its old communications channels with their opposite numbers in other countries, now that it controls a state with its own official channels? Probably, in some cases. The old connections elicited accusations of meddling. I recall the sharp-witted Saudi Foreign Minister, Prince Saud Al Faisal, once telling the Iranians: "If you want us to work together in serving Arab causes, don't come to us through back doors, use the front door to come into the house. Why are your links invariably with factions within nations?"

Jamal Khashoggi is editor-in-chief of the planned Alarab news channel.

On Twitter: @JKhashoggi

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