Mexico's next president, Andrés Manuel López Obrador, addresses supporters in Mexico City on Sunday. (Edgard Garrido/Reuters)

ANDRÉS MANUEL LÓPEZ OBRADOR, who on Sunday was elected in a landslide to be Mexico’s next president, is a product of the political left, but his victory is part of the global story of rising populist leaders. Like many of them, including President Trump, Mr. López Obrador promises to overturn the reigning political establishment, says he alone is capable of delivering on his far-fetched promises, and assails the media, courts, civil society groups and all others who might check his personal power. Like other populists, the incoming Mexican leader also has been vague and occasionally contradictory about the specific policies he may pursue, even while insisting he will bring about a “transformation” comparable to Mexico’s achievement of independence. In that, he is sure to fail; the question is how much damage he may do to the democratic system that enabled him to gain power.

Having refused to accept defeat in a previous presidential bid, Mr. López Obrador claimed without evidence that this year’s election could be stolen from him. But the vote was free and fair, and his establishment rivals quickly and gracefully conceded defeat. The new party the president-elect created likely won a majority in both houses of Congress, giving him more power than any executive since Mexico’s quasi-autocratic rulers before the turn of the century. The scale of the triumph is less reflective of mass support for a 64-year-old career politician than mass rejection of Mexico’s traditional parties, which serially failed in the past two decades to curb rising violence and endemic corruption or to nurture rapid economic growth.

Mr. López Obrador has vowed to “eliminate, not reduce,” corruption, though he has not said how he would do it, other than by setting a good personal example. Similarly, he has not explained how he would bring down the soaring murder rate, though he has hinted at legalizing some narcotics. He has promised tens of billions of dollars in new spending on social programs while claiming he will not add to Mexico’s debt. He is no more likely to pull that off than was Mr. Trump in pledging to cut taxes without increasing the budget deficit.

It may be that Mr. López Obrador’s promise of radical reform will amount to reversing the hard-won progress of his predecessors in shifting the statist, autocratic Mexico of the 20th century toward a modernizing liberal democracy. The new president has promised to reverse a landmark educational reform and is likely to slow a partial privatization of the oil industry. He says he will build up Mexican agriculture and refining, which would curtail imports from the United States. Though he now says he favors preserving the North American Free Trade Agreement, Mr. López Obrador is an unlikely savior of an accord the Trump administration is seeking to hollow out.

Other governments, especially in Latin America, should guard against any steps by Mr. López Obrador to erode democratic institutions and media freedoms. Though he may prove pragmatic in office, the new president has made Mexicans some very large promises. That raises the question of what he and his followers will do once it becomes clear that he cannot deliver.