The legislation is the result of a congressional compromise reached at the weekend and is aimed at punishing the Kremlin for meddling in the 2016 US presidential election and Russia's annexation of Crimea.
But it could end up penalizing European firms that contribute to the development of Russia's energy sector.
New sanctions against Iran and its Islamic Revolutionary Guard Corps, which stands accused of supporting terrorism, and North Korea, for its missile tests, are also included in the bill.
The vote is expected around 5:00 pm (2100 GMT).
"The House will vote on bipartisan legislation to hold Russia, Iran and North Korea accountable for their aggression," said congressman Ed Royce, chairman of the House Foreign Affairs Committee.
Key among the provisions is one that handcuffs the US president by making it difficult for him to unilaterally ease penalties against Moscow in the future -- effectively placing him under Congress's watch.
Initially, Trump resisted the legislation. But faced with near-total consensus among Republican and Democratic lawmakers, the White House blinked, but did not say directly that the billionaire president would sign it into law.
"He's going to study that legislation and see what the final product looks like," spokeswoman Sarah Sanders told reporters Monday on Air Force One.
Veto likely not effective
In mid-June, the Senate voted 98-2 in favor of tough sanctions on Moscow and Tehran, but the text stalled in the House.
Now that an agreement has been reached, the House vote could be similarly overwhelming.
The measure would then return to the Senate for final passage, likely before summer break begins in mid-August.
US lawmakers, including Republican leaders, have remained wary of the intentions of the billionaire businessman-turned-president -- who has called for better relations with Moscow -- regarding a relaxation of pressure on Putin.
But even if Trump were to veto the legislation, Congress would likely be able to overcome such a blockage with a two-thirds majority in each chamber.
Russia says sanctions 'counterproductive'
The Kremlin warned that fresh sanctions on Russia would adversely affect both sides.
"We consider such a continuation of the rhetoric of sanctions counter-productive and harmful to the interests of both countries," Kremlin spokesman Dmitry Peskov said Monday.
From Paris to Berlin, the sanctions bill was seen as a unilateral action by Washington that disrupts a carefully crafted order.
To date, sanctions against Moscow have been coordinated on both sides of the Atlantic, to maintain a united front.
"For us, G7 unity regarding sanctions is of key importance," European Commission spokesperson Margaritis Schinas said.
European Union member states were due to meet Wednesday and discuss the issue -- and a possible response.
Several European nations including Germany are livid because the new law would allow the punishment of companies working on pipelines from Russia, for example by limiting their access to US banks.
The provision could theoretically pave the way for sanctions against the European partners in Nord Stream 2, a project to build a pipeline carrying Russian gas across the Baltic which could boost supplies to Germany from 2019.
Such partners include France's Engie, Germany's Uniper and Wintershall, Austrian firm OMV and the Anglo-Dutch Shell.
To date, Washington and Brussels had agreed that sanctions would not affect Europe's gas supply.
In an apparent concession, the House slightly modified a provision so that the bill only targets pipelines originating in Russia, sparing those which merely pass through that nation, such as the Caspian pipeline which carries oil from Kazakhstan to Europe.