The world’s biggest search engine announced the change in a blog post on its website.
The move has been welcomed by record companies in the UK and Hollywood film studios.
Movie and music firms have complained in the past that Google should have been doing more to fight piracy.
They say searching for an artist, song or film often brings up pages of illegal sites, making it hard to find a place to download a legal version.
From next week, search results will take into account the number of “valid copyright removal notices”.
Sites with more notices will rank lower, although Google has not said what it considers a valid notice.
The BPI, which represents record labels in the UK, has welcomed the news.
Chief executive Geoff Taylor said: “We have argued for some time that sites with a lot of illegal content should feature lower in search rankings, based on the notifications we send to Google.
“Consumers overwhelmingly want and expect the top search results for entertainment content to feature legal, licensed services.
“We will look carefully at how much impact this change will have in practice, but we welcome the announcement from Google and will be pressing other search engines to follow suit.”
The Motion Picture Association of America (MPAA) said it was “optimistic” about the changes.
“We will be watching this development closely – the devil is always in the details,” said MPAA senior executive president Michael O’Leary.
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