Muhammadu Buhari, Nigeria’s president-elect, did not smile while making his acceptance speech on Wednesday — understandably, as terrorism and corruption were his main talking points.

A day after piling up substantial vote totals against the incumbent president, Mr. Buhari, a former general who once rose to power in a military coup, further consolidated something extraordinary for Nigeria: the peaceful passing of power from one political party to another through the ballot box, according to New York Times.

The country is now a democratic nation like others, Mr. Buhari suggested Wednesday, both in his words and in the fact that the democratic process had worked well enough that he could give the speech at all.

But in his remarks in the Nigerian capital, Abuja, Mr. Buhari also bluntly enumerated two scourges in this giant democracy: the ruthless onslaught of the Boko Haram militant group and the “evil of corruption,” as he put it.

In pairing them so prominently, he appeared to be setting his agenda for the coming months. And in lieu of a detailed policy platform from Mr. Buhari, who was short on specifics during his campaign, his vow to defeat Boko Haram amounts to a national security strategy, while fighting corruption has become an economic one.

President-elect Muhammadu Buhari, a former military leader, vowed to fight the scourges of corruption and Boko Haram militants.

On Wednesday, he focused more on the challenges posed by corruption than on the dangers of Boko Haram, perhaps indicating a veteran soldier’s disdain for the group as a true military threat.

Though Boko Haram has killed thousands of civilians and stormed across big stretches of territory, Mr. Buhari was bluntly dismissive of the insurgents in a January interview on the campaign trail, characterizing their fighting abilities in disparaging terms.

“Boko Haram will soon know the strength of our collective will,” he said Wednesday. “We shall spare no effort until we defeat terrorism.”

As a practical matter, Boko Haram, despite having pledged allegiance to the Islamic State terrorist group, is now less of a menace on the ground in Nigeria than it was in January.

A coalition of foreign and domestic troops has substantially reduced Boko Haram’s footprint in the northeastern territory it had been holding for much of the past few years. Troops from Chad have taken the handful of border towns once held by the militants, and the Nigerians, backed by South African mercenaries, have taken others.

It is impossible to verify the Nigerian military’s claim that nearly all the previously Islamist-occupied towns in the northeast — “local government areas,” as they are called in Nigeria — have now been reclaimed from Boko Haram. But many have been, and the latest, Gwoza, had been a Boko Haram stronghold for months.

More challenging for Mr. Buhari will be the rot in the army that led to Boko Haram’s ascendance in the first place: corruption at high levels, poor morale, and troops underequipped because much of the $6 billion military budget has apparently been diverted.

“What they have is such an institutional problem, it’s going to take a long time to fix it,” said a diplomat in Abuja, who was not authorized to speak publicly. The hiring of mercenaries to defeat Boko Haram is a “short- to mid-term solution until they can address the other thing,” the diplomat said.

In interviews, Mr. Buhari has spoken of his anger at seeing foreign troops play a leading role in solving Nigeria’s Boko Haram problem. But he may not have much choice for now.

Most difficult for him will be how to handle the command deficiencies that put frightened, lightly armed soldiers in the field against Boko Haram, leading to many losses and retreats in Nigeria’s nearly six-year battle with the militants.

Human rights abuses against civilians by the Nigerian military have also been disturbingly common, with soldiers killing and detaining residents en masse.

“What has been consistently lacking is the required leadership in our battle against insurgency,” Mr. Buhari said in a speech at the London think tank Chatham House in late February.

Here, he will tread gingerly, Mr. Buhari has suggested, seeking to determine responsibilities before proceeding to, say, firing the top chiefs whom many blame for Nigeria’s military failures.

Boko Haram led Mr. Buhari on Wednesday to segue immediately into Nigeria’s corruption problem, which “attacks our national character” and “distorts the economy,” he said.

He made it clear that, falling oil prices aside, he sees this as the country’s top economic problem, telling the audience at Abuja’s International Conference Center that “such an illegal yet powerful force soon comes to undermine democracy.” He promised to “end this threat to our economic development and democratic survival.”

At Chatham House, Mr. Buhari suggested that what he called a “war waged on corruption” would be the first step in tackling the country’s pressing economic problems.

The price of oil, on which the government depends for over 70 percent of its revenue, has tumbled. Nigeria’s currency has fallen some 20 percent against the dollar over six months. Foreign currency reserves are dwindling, and an oil-revenue rainy day fund has been ransacked.

“In the face of dwindling revenues, a good place to start the repositioning of Nigeria’s economy is to swiftly tackle two ills that have ballooned under the present administration: waste and corruption,” Mr. Buhari said at Chatham House.

Several Nigerian economists suggested that Mr. Buhari’s strategy was plausible as a first step.

“The first thing to do is to recognize that there is so much waste in government,” said a leading Lagos economist, Pat Utomi.

“If you cut the graft, you can do things,” he said. “We have a new presidential jet in this budget. Most airlines in Nigeria don’t have as many jets as the presidential fleet.”

Another economist also suggested that Mr. Buhari’s anticorruption stance was critical in a country with, as a recent World Bank paper put it, a “deeply embedded culture of corruption.”

With the new president’s emphasis on “accountability, integrity and transparency,” one economist, Bismarck Rewane, said the “missing piece in the Nigerian economy” would be filled in.

Of course, other Nigerian politicians have promised to end corruption, only to fail or even steal with abandon afterward. But there is some reason to think Mr. Buhari may hew more closely to his promises. As military ruler in 1984 and 1985, he did not enrich himself. And he ruthlessly pursued those whom he accused of corruption.

“Corruption will not be tolerated by this administration, and it shall no longer be allowed to stand as if it is a respected monument in this nation,” he said Wednesday.