The bill, which received overwhelming support in the Russian parliament on Friday, also applies to information about public figures and information considered to be in public interest.
In practice, Internet search engines would need to remove the search results which are "untrustworthy," "no longer relevant," or "distributed in violation of the law," at a personal request.
Before the vote, lawmaker Leonid Levin announced that the legislation "will create an efficient tool for clamping down on blackmail and Internet bullying." He also denied accusation that it could be used to silence criticism of the government, saying that the law does require original posts on websites to be deleted.
The bill also expands the jurisdiction of Russian courts to foreign search engines, as long as they are running ads targeting Russian users. It is set go into power in January 2016, after being signed by President Vladimir Putin.
No more 'best before' date
The law provoked criticism from various Internet companies after its introduction in late May. Russia's most popular search engine Yandex complained that a right to be forgottent initiative like this, "ignores the right to search."
"This bill impedes people's access to important and reliable information, or makes it impossible to obtain such information," Yandex said in a statement last month.
However, the version of the law approved on Friday features several corrections suggested by the industry representatives. Most notably, the law does not see information older than three years as "outdated." Earlier drafts of the bill gave users grounds to seek its removal.
The search engines would also have ten working days to reply to a deletion request, and not three, as previously suggested.
Commenting on the final version of the law, Yandex said on Friday that "many important changes, from our point of view, have not been implemented."
EU protecting online privacy
The bill comes in the wake of worldwide debate on what search engines should and can tell their users, and what constitutes protection of personal data.
Last year, the EU's top court ruled that users had the "right to be forgotten" and could request the search engines like Google remove links to personal information that are "inadequate, irrelevant... or excessive." In June 2015, EU justice ministers pushed for more privacy and protection for users online.
However, under the EU legislation, personal information cannot be deleted if deemed to be in public interest.
dj/msh (Reuters, AFP, Interfax, AP)