Adopting a more serious tone, he went on to say: "I know some of you are curious about the breakup, but the truth is, it's nobody's business and sometimes things just don't work out and that's OK. She is a wonderful, strong person and I genuinely wish her all the happiness in the world."
Davidson, 24, and Grande, 25, got engaged in June after a few weeks of dating, but broke up last month.
Davidson said on SNL in September that he had been living in Grande's luxurious New York apartment where his only responsibility is stocking the fridge.
He joked at the time that he wanted a pre-nuptial agreement.
"God forbid we split up and she takes half my sneakers," he said.
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Celebrity breakups of 2018