Former Hungarian Prime Minister Viktor Orban’s spectacular landslide defeat last month has been interpreted as a setback for the European right. It is not. Rather, it is the most recent signal of a deeper trend in the democratic West: the transformation of the far right into a populist-inflected conservatism.

Sworn in as Orban’s successor on May 9, Peter Magyar is neither a liberal nor a centrist. He waged an election campaign from the moderate right, retaining a populist emphasis on national sovereignty, national identity, and strict control over immigration. Rather than challenge populist and conservative themes, he focused his attacks on Orban’s centralization of power, rigging of the electoral system, and growing cronyism and corruption.

Former Hungarian Prime Minister Viktor Orban’s spectacular landslide defeat last month has been interpreted as a setback for the European right. It is not. Rather, it is the most recent signal of a deeper trend in the democratic West: the transformation of the far right into a populist-inflected conservatism.

Sworn in as Orban’s successor on May 9, Peter Magyar is neither a liberal nor a centrist. He waged an election campaign from the moderate right, retaining a populist emphasis on national sovereignty, national identity, and strict control over immigration. Rather than challenge populist and conservative themes, he focused his attacks on Orban’s centralization of power, rigging of the electoral system, and growing cronyism and corruption.

In a sharp challenge to Orban’s authoritarian rule, Magyar made the case for checks and balances and the rule of law, called for an end to government dominance over the media, and rejected Orban’s role as Europe’s spoiler. Instead of anti-Brussels rhetoric, Magyar argued for the constructive defense of Hungary’s sovereignty and national interests inside European Union and NATO institutions. Above all, he repudiated Orban’s dalliance with and reliance on Moscow, soberly seeing Russian President Vladimir Putin’s regime as a threat to European peace and security.

Magyar’s electoral approach was not a one-off: It reflects an evolving populist conservatism that is taking root in Britain, France, Italy, to some extent Poland, and elsewhere. This new conservatism reflects the mellowing of far-right populist parties and echoes Magyar’s more moderate but electorally popular nationalism.

A crowd gathers to watch the first session of parliament on the day Magyar is sworn in in Budapest on May 9.John Moore/Getty Images

A little over a decade ago, right-wing populists such as Britain’s Nigel Farage, France’s Marine Le Pen, Italy’s Giorgia Meloni, and Hungary’s Orban were viewed in many liberal precincts as the second coming of 1930s-style fascism. There were ample reasons for concern, especially because the European populist right attracted a core of identitarian activists who admired fascist and other radical right thinkers from the 1920s and 1930s. Far-right rhetoric was suffused with racism, antisemitism, and contempt for democracy.

Many leading right-wing European parties, moreover, admired Putin and sometimes established close relationships with the Kremlin. Le Pen’s party received a loan from a Czech-Russian bank in 2014. That same year, Italian Deputy Prime Minister Matteo Salvini—then a member of the European Parliament—was photographed in Red Square wearing a Putin T-shirt. And Farage’s successful Brexit campaign attracted agents and admirers of Putin’s regime, one of whom was recently sentenced for accepting Russian bribes when he was an MEP.

As these parties gained force in the aftermath of the 2008 financial crisis and amid increased migration from........

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