And so, after six long decades of military rule, Egypt has a democratically elected, civilian President at last. For all the shenanigans of the past week – the sudden dissolution of the Muslim Brotherhood-dominated parliament, the sweeping powers arbitrarily grabbed by the ruling military council, the rumour and counter-rumour over the failing health of Hosni Mubarak – nothing can detract from the scale of Egypt's achievement. A broadly free and fair election, as this would appear to have been, is a seminal moment not just for Egypt, but for the Arab Spring and the world beyond.

The outcome itself is also a matter of some relief. The much-delayed final tally, granting the Muslim Brotherhood's Mohamed Morsi a convincing victory, was met with jubilation by thousands of supporters thronging Cairo's Tahrir Square. But there was an all-too real threat of violence had Mr Morsi's widely-anticipated win been handed to his rival, the former air force commander and Mubarak Prime Minister, Ahmed Shafik. And, notwithstanding concerns over Mr Morsi's Islamism, a Shafik victory – even a fair one – would have looked too much like a return to the old order.

For all the jubilation, however, Egypt's challenges are far from over. Indeed, they may be just beginning. Not the least of Mr Morsi's immediate priorities is the poor state of the economy. The turmoil of the last 16 months has been devastating: tourism has slumped, foreign exchanges reserves are dwindling, and the government's finances are in dire straits. Meanwhile, unemployment is high and rising, particularly among young people. Near the top of Mr Morsi's agenda, therefore, must be the International Monetary Fund support turned down by the military council last year. But over the longer term, alongside such concerns as healthcare and education, the new President will need to institute wide-ranging economic reforms to tackle the sclerosis caused by decades of cronyism.

As if all that were not difficult enough, Mr Morsi must also grapple with a whole suite of far-reaching constitutional issues. Some are broad: what, for example, is to be the relationship between sharia and secular law in the new Egyptian state? Others are more immediate, but no less tricky, of which the most pertinent must be the vexed question of Egypt's as-yet-unwritten constitution. It is here that the struggle with the so-called "deep state" will be in sharpest relief. Indeed, Mr Morsi may now be President in name, but, after last week's shock constitutional declaration from the SCAF, he is set to have no control over Egypt's budget, its foreign policy, or its army. The military council has also reserved to itself the power to select the committee to draft the constitution, and parliament will not be re-elected until after it is in place. Mr Morsi will, therefore, need to fight for the powers of the presidential office and for a constitution that ensures that military power comes second to that of civilian political institutions.

It will be quite a fight. And, for all the agitations from the Muslim Brotherhood in recent days, there is real concern that they and their candidate may not be as different as their promises suggest. The party has already seen public support dip, after its parliamentary success, amid accusations of a factionalism and ineffectiveness. The danger is that the Brotherhood's tendency to make a lot of noise, while doing a deal behind the scenes, sees Mr Morsi duck his most fundamental responsibility – which is to live up to the ideals of Tahrir Square and unravel the web of power and corruption in which the country has so long been caught.

Egypt's problems cannot hope to be tackled all at once. But Mr Morsi does not have long to prove that he is up to the job. All the world is watching.