The pop track broke into the top 40 two weeks ago at number 37, four weeks after its release, and has been climbing steadily, ending up at number three in last week's chart.
The video that accompanies the single has amassed more than 253 million views in just two months and became the most "liked" video of all time on YouTube.
Psy, who is already an established star in South Korea having released six albums, taught Britney Spears his dance moves on US TV show Ellen earlier this month.
The track knocks last week's number one, Irish band The Script, off the top spot to number two with their single Hall of Fame, featuring Will.i.am of the Black Eyed Peas.
American rapper Flo Rida rounds off the top three with his single I Cry.
There were no newly-released songs in the Official UK Charts Company top 10 singles, with the highest-reaching new entry being DJ Fresh's The Feel at number 13.
Meanwhile folk four-piece Mumford And Sons have gone straight to the top of the album chart with their new release Babel. It follows their 2009 award-winning debut, Sigh No More, which also reappears in the top 40 this week at number 10.
The number two spot is also taken by a new entry - punk rockers Green Day.
The Californian act, who first enjoyed mainstream success in the mid-90s, stormed in to second place with Uno, the first of a trilogy of albums with Dos and Tre to follow soon.
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