Article I, Section 8 of the Constitution specifically gives Congress the responsibility for setting tariffs.
However, Congress has a long history of being uncomfortable with the responsibility. This discomfort first shows up in 1934 with the Reciprocal Trade Agreement Act of 1934. The act gives the President essentially free rein to set or modify tariffs at any time as long as he finds that existing duties are "unduly burdening and restricting the foreign trade of the United States". The authority given expires 3 years after the date of enactment.
In 1962, the country embarked on another such experiment with the Trade Expansion Act of 1962. This act required the President to make same finding as in the 1934 act. This act expired after 5 years, and it included limits placed on the amount of change the President was authorized to make. It also included extensive provisions to allow indiviual businesses or unions to file for relief.
In 1974, Congress got away from giving powers to the President, and instead created a whole new Office of the United States Trade Representative. This approach hopefully got around the basic problem of Congress's inability to act quickly by giving the new office the job of handling all the negotiations, with the guarantee that Congress would be able to approve or disapprove the final proposal quickly, and without any opportunity to make changes.
The final legislation involved in this story is the International Emergency Economic Powers Act of 1977. It actually has nothing to do with tariffs but has gotten drug into the discussion, since Trump or his legal team, apparently fell in love with the concept given in the first section of the act, and never bothered to read the second section to find out what powers it actually conveyed.
The IEEP Act of 1977 gave the President power to declare a national emergency as a result of an "unusual and extraordinary threat from without the country effecting our national security, foreign policy, or economy". If the President declares such a threat then he is authorized to "investigate, regulate or prohibit" foreign exchange transactions, foreign payments, and exporting of currency or securities. In other words, basically freeze all liquid assets moving in or out of the country. That is a terrifing possibility, but Trump only wanted to use it with regard to tariffs. So, when he was sued back in 2025 because of the tariffs he used the IEEP Act as his defense. The U.S. Court of Appeals pointed out that the subject law has nothing to do with tariffs. They accordingly found the Trump tarriffs unconstitutional back in 08/2025. It was appealed to the Supreme Court on 9/3/2025, and argued on 11/5/2025. The Supreme Court is still sitting on it. It has been combined with previous cases and can now be found under docket 24-1287.
The common thread here is the tendency of Congress to give away extremely import powers. I think the Office of the United States Trade Representative is an exception here as the powers seem to be given completely, and with a complete structure attached to allow Congress to have the final say. By contrast, the powers given to the President are conditional, but the condition is vague enough as to allow the President to claim it exists whenever he wants.
I would submit that the underlying problem here is that the Congress has been given detailed responsibilities, yet they work to a tune that is not capable of quick response. The only guidance given by the Constitution on this score is "Each House may determine the Rules of its Proceedings", from Article 1, Section 5.