The measure, finalised on Friday, was a last legacy item for the late senator Lindsey Graham, a close ally and friend of Trump who had just returned from Ukraine when he unexpectedly died in July.
In the works for more than a year, the bill passed with large bipartisan margins: 86-11 in the Senate and 262-159 in the House.
It is meant to starve Russian President Vladimir Putin of the resources Moscow needs to continue its war in Ukraine after invading its neighbour more than four years ago.
The bill sanctions Russian officials, banks and a shadow fleet of tankers that keeps Russian energy moving.
It also directs Trump to impose up to 100 per cent tariffs on the top five importers of Russian oil or natural gas, with an exception for countries that import less than 15 per cent of Russia's natural gas exports and have taken significant steps to reduce those imports.
Despite overwhelming support on Capitol Hill, the legislation faced criticism from a vocal set of Democratic lawmakers who warned Trump could use his new expanded tariff powers to impose fresh levies in the European Union and elsewhere.
Graham's journey to getting Trump's sign-off on the bill had been full of fits and starts, as the White House had to be convinced that the president would be able to retain sufficient flexibility on sanctions.
Eventually, Trump gave a nod to the bill after it included his push for a five-year extension of existing sanctions on Iran.
