The law, which has sparked outrage among Russian liberals and children's rights advocates, takes effect on January 1. Washington has called the law misguided and said it ties the fate of children to unrelated political considerations.
It is likely to deepen a chill in US-Russian relations and deal a blow to Mr Putin's image abroad.
Russia's child rights commissioner, Pavel Astakhov, has reportedly said that 52 children whose adoptions by American parents are under way will remain in Russia.
The law will also outlaw some non-governmental organisations that receive US funding and impose a visa ban and asset freeze on Americans accused of violating the rights of Russians abroad.
Pro-Kremlin politicians initially drafted the bill to mirror the US Magnitsky Act, which bars entry to Russians accused of involvement in the death in custody of anti-corruption lawyer Sergei Magnitsky and other alleged rights abuses.
The restrictions on adoptions and non-profit groups were added to the legislation later, going beyond a tit-for-tat move.
Mr Putin's spokesman said the Magnitsky Act had seriously undermined the "reset" – the effort launched by US President Barack Obama early in his first term to improve relations between the former Cold War foes.
Mr Putin has backed the hawkish response with a mix of public appeals to patriotism, saying Russia should care for its own children, and belligerent denunciations of what he says is the US desire to impose its will on the world. Seeking to dampen criticism of the move, Mr Putin also signed a decree ordering an improvement in care for orphans.
The acquittal last Friday of the only person being tried over Mr Magnitsky's death will fuel accusations by Kremlin critics that the Russian authorities have no intention of seeking justice in a case that has blackened Russia's image.
A Russian court acquitted Dmitry Kratov, the former deputy head of a jail where Mr Magnitsky was held before his death in 2009 after nearly a year in pre-trial detention, after prosecutors themselves dropped charges against him. Lawyers for Mr Magnitsky's family said they would appeal and called for further investigation.
Mr Magnitsky's colleagues say he is the victim of retribution from the same police investigators he had accused of stealing $230 million from the state through fraudulent tax refunds – the very same crimes with which he was charged.
The case against Mr Magnitsky was closed after his death but reopened again in August 2011.
In an unprecedented move, Russia is trying him posthumously for fraud, despite protests from his family and the lawyers that it is unconstitutional to try a dead man. A preliminary hearing is scheduled for next month.
Mr Magnitsky's death triggered an international outcry and Kremlin critics said it underscored the dangers faced by Russians who challenge the authorities. The Kremlin's own human rights council said Mr Magnitsky was probably beaten to death.
The adoption ban may further tarnish Mr Putin's international standing at a time when the former KGB officer is under scrutiny over what critics say is a crackdown on dissent since he returned to the Kremlin for a six-year third term in May.