The new penalties are aimed at rebuking Moscow for interfering in the 2016 presidential election and its military aggression in Ukraine and Syria.
Lawmakers voted 419-3 to pass the bill, which prevents President Donald Trump from waiving the sanctions against Russia without first securing permission from Congress.
The measure now heads to the Senate for action. The bill could be sent to Trump before Congress begins its August recess.
The legislation also would slap penalties on Iran and North Korea.
Trump hasn’t threatened to reject the bill, but senior administration officials had objected to the requirement for a mandated congressional review should the president attempt to ease or lift the Russia sanctions. They argued the review infringes on the president’s executive authority.