BRUSSELS—European Union regulators opened a formal probe into Amazon.com Inc.’s tax arrangements in Luxembourg, snaring another major U.S. company in a high-profile investigation that has already targeted Apple Inc. and Starbucks Corp.

The investigation marks the latest phase in a broader clampdown on tax avoidance by multinationals in Europe, where governments and regulators are seeking to bolster revenues and address concerns that big international groups have an unfair advantage over local companies.

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