The investigation is being conducted by federal prosecutors in Delaware. US media quote sources saying it relates to business dealings with foreign countries including China.
Hunter Biden said he was confident he would be shown to have done no wrong.
The Biden-Harris transition team said the president-elect was "deeply proud of his son".
A statement from the team said Hunter had "fought through difficult challenges, including the vicious personal attacks of recent months, only to emerge stronger".
The 50-year-old said he had learned of the investigation on Tuesday. He did not disclose any further details.
"I take this matter very seriously but I am confident that a professional and objective review of these matters will demonstrate that I handled my affairs legally and appropriately, including with the benefit of professional tax advisers," he said.
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