ROME—Italian voters on Sunday rejected constitutional changes backed by the government, prompting Prime Minister Matteo Renzi to announce his resignation and handing populists a victory in the heartland of Europe.

With virtually all the votes counted early Monday, 59.6% were “no,” according to Italy’s Interior Ministry, marking a stinging rebuke to Mr. Renzi’s plan to overhaul Italy’s legislature to make it easier to pass laws, including measures meant to make the country more competitive.

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