The Criminal Finances Bill, which cleared the Commons on Tuesday, is meant to freeze the assets of foreign officials who abuse anti-corruption and human rights activists.
The law was prompted by the case of Russian lawyer Sergei Magnitsky.
He died in prison after revealing alleged fraud by state officials.
Mr Magnitsky,  legal adviser for London-based Hermitage Capital Management (HCM), had been jailed after he was accused of committing fraud himself. Supporters say his death in November 2009 was the result of a severe beating, but official records say he died of acute heart failure and toxic shock, caused by untreated pancreatitis.
Since his death, HCM's founder William Browder has been campaigning to bring to justice those he believes are responsible for what happened to Mr Magnitsky.
He had already managed to get the US to sign the Magnitsky Act into law in 2012, which promise to deny visas to and freeze assets in the US of 18 people linked to the lawyer's death by Mr Browder's investigation.
On Tuesday, he welcomed the third reading of the UK bill in the Commons as a "huge triumph" that would "cause perceptible fear for kleptocrats in Russia and other authoritarian regimes".
"They all have expensive properties in London and think they are untouchable," he said in a statement.
Speaking during the bill's reading, Security Minister Ben Wallace said: "We need to make the UK a hostile environment for those seeking to move, hide and use the proceeds of crime and corruption. In an increasingly competitive international marketplace, the UK simply cannot afford to be seen as a haven for dirty money."
He added: "This measure would send a clear statement that the UK will not stand by and allow those who have committed gross abuse or violations around the world to launder their money here."
The bill must now make its way through the Lords.
A bill inspired by the case of a Russian whistleblower will turn the UK into a "hostile environment" for organised criminals and kleptocrats.