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"If you'll permit one sincere, un-ironic tweet: I hope President-elect Trump proves to be a far better president than I had expected," Kristol tweeted.
The Weekly Standard editor added: "And to my fellow #NeverTrumpers: Let us be magnanimous losers."
Kristol, a prominent proponent of neoconservatism and former chief of staff to Vice President Dan Quayle, had been extremely critical of Trump throughout the 2016 campaign cycle.
The Associated Press declared Trump the president-elect at 2:30 a.m. ET, shortly after the wire service placed Wisconsin in his column.
Trump's victory was one of the most stunning political upsets in history. Clinton was strongly favored to emerge as the victor on Tuesday night, with some analysts estimating Trump's odds of winning the election as low as 1%.