The move comes after a landmark European Union court ruling earlier this month, which gave people the "right to be forgotten".
Links to "irrelevant" and outdated data should be erased on request, it said.
Google said it would assess each request and balance "privacy rights of the individual with the public's right to know and distribute information".
"When evaluating your request, we will look at whether the results include outdated information about you, as well as whether there's a public interest in the information," Google says on the form which applicants must fill in.
Google said it would look at information about "financial scams, professional malpractice, criminal convictions, or public conduct of government officials" while deciding on the request.
Earlier this month, the BBC learned that more than half of requests sent to Google from UK individuals involved convicted criminals.
This included a man convicted of possessing child abuse images who had also asked for links to pages about his conviction to be wiped.'Fraudulent requests' Continue reading the main story “Start Quote
As we regulate the internet, I think we're not going to see the kind of innovation we've seen”End Quote Larry Page Google
On 13 May, the EU's court of justice ruled that links to "irrelevant" and outdated data on search engines should be erased on request.
The case was brought by a Spanish man who complained that an auction notice of his repossessed home, which appeared on Google's search results, infringed his privacy.
On Friday, Google said that EU citizens who want their private details removed from the search engine will be able to do so by filling out an online form.
However, they will need to provide links to the material they want removed, their country of origin, and a reason for their request.
Individuals will also have to attach a valid photo identity.
"Google often receives fraudulent removal requests from people impersonating others, trying to harm competitors, or improperly seeking to suppress legal information," the firm said.
"To prevent this kind of abuse, we need to verify identity."Less innovation?
However, in an interview given to the Financial Times, Google boss Larry Page said that although the firm would comply with the ruling, it could damage innovation.
He also said the regulation would give cheer to repressive regimes.
Mr Page said he regretted not being "more involved in a real debate" about privacy in Europe, and that the company would now try to "be more European".
But, he warned, "as we regulate the internet, I think we're not going to see the kind of innovation we've seen".
Mr Page added that the ruling would encourage "other governments that aren't as forward and progressive as Europe to do bad things".A right to be forgotten? In 2012, the European Commission published plans for a "right to be forgotten" law, allowing people to request that data about themselves to be deleted Online service providers would have to comply unless they had "legitimate" reason to do otherwise The plans are part of a wide-ranging overhaul of the commission's 1995 Data Protection Directive UK's Ministry of Justice claims that the law "raises unrealistic and unfair expectations" Some tech firms have expressed concern about the reach of the bill
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