The first-person puzzle-platform title also won the awards for best design and best story.
Dice's Battlefield 3 secured a prize voted for by the public, as well as for the best online multiplayer game.
Other award winners included Batman: Arkham City for action, Little Big Planet 2 for game innovation and LA Noire for best original music.
Josh Weier, Portal 2's project leader, seemed slightly startled to follow up his team's victory at October's Golden Joystick awards.
"I've had about three hours of sleep and a whole lot of jet lag so I'm going to try to be brief before I go off the rails," he said.
"It was a real pleasure working on this game and it's just amazing to be here tonight and win this award."
Markus "Notch" Persson - the creator of Minecraft - was also honoured with a special award.
His unique environment-building title has generated more than five million sales despite lacking a third-party publisher and marketing campaign.
"Wow," the 32-year old said on taking to the stage.
"This is obviously huge. To have such a serious thing like this [event] celebrating games is very good - who else would do it but the British."
The ceremony included a total of 19 prizes, including four new categories: debut game, online-browser, online-multiplayer and performer.
