The Lindsey Graham Act -- named after the deceased US senator who sponsored the bill -- allowed Trump the authority to impose duties up to 100 percent on major buyers of Russian oil and gas.
"As described further in section 4 of this order, I am hereby waiving the application of such sanctions, restrictions, and duties provided for in the Graham Act," the executive order said.
The law targeted Russia's energy and defense sectors, President Vladimir Putin and other senior officials, as well as Moscow's so-called shadow fleet of tankers used to circumvent Western sanctions.
Trump's reversal on the Russia sanctions comes in after a controversial deal he struck with Putin that would allow Russia diesel exports in exchange for US sanctions relief.
Relations between Kyiv and Washington have soured since the deal, with Ukrainian President Volodymyr Zelensky calling it a "weak decision" and Ukrainian forces resuming attacks on Russian oil refineries.
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