The bill, which also brings sanctions against Iran and North Korea, was described as “seriously flawed” by US President Donald Trump.
But Congress voted for it by such an overwhelming majority that he was unable to veto it.
President Trump’s anger was mirrored in Moscow, where Russia’s prime minister Dmitry Medvedev wrote on Facebook that the bill would bring “consequences”.
He said: “First, it ends hopes for improving our relations with the new US administration.
“Second, it is a declaration of a full-fledged economic war on Russia.
“Third, the Trump administration has shown its total weakness by handing over executive power to Congress in the most humiliating way.
“This changes the power balance in US political circles.”
The Foreign Minister went further, predicting the President’s imminent demise.
He wrote: “What does it mean for them?
“The US establishment fully outwitted Trump; the President is not happy about the new sanctions, yet he could not but sign the bill.
“The issue of new sanctions came about, primarily, as another way to knock Trump down a peg.
“New steps are to come, and they will ultimately aim to remove him from power.
“A non-systemic player has to be removed.”
Mr Trump had vowed to warm relations between Washington and Moscow and he had anticipated a free hand on foreign affairs.
The lesson from Capitol Hill is the latest in a difficult political awakening for the President.
Fracture lines are growing between his Republican administration and legislators and his frustration showed in a statement in which he criticised Congress after the sanctions bill was passed.
He said: “The bill remains seriously flawed – particularly because it encroaches on the executive branch’s authority to negotiate.
“Congress could not even negotiate a healthcare bill after seven years of talking.
“By limiting the Executive’s flexibility, this bill makes it harder for the United States to strike good deals for the American people, and will drive China, Russia, and North Korea much closer together.
“The framers of our Constitution put foreign affairs in the hands of the President.
“This bill will prove the wisdom of that choice.
“I built a truly great company worth many billions of dollars… as President, I can make far better deals with foreign countries than Congress.”
The key problem regarding Mr Trump and Russia was, well, Mr Trump and Russia.
Washington is agog at almost daily developments on the allegations that the Trump election campaign colluded with Russia to support his bid for the Presidency.
Expecting a free pass to deal with Moscow on his terms, and his terms alone, was asking for too much trust.