The duo finished third on the last season of BGT during a finale which saw their final performance marred by a woman who crashed the stage to throw eggs at the judges.
Now, however, they have something to smile about!
Richard and Adam seemed stunned by their success, telling the Official Chart Company it was a "dream come true" to top the UK chart.
"You've made us happy, and you've made our nan extremely happy, so thank you to each and everyone of you who's bought the album," added Adam.
The pair, who hail from Holywell, north Wales, later added on Twitter: "We don't know what to say, words are not enough to thank you all."
Richard & Adam signed a multi-album deal with Sony just after Britain's Got Talent.
It's been a good couple of weeks for reality show contestants in the album charts: last week, X Factor runner-up Jahmene Douglas scored the top spot with his Love Never Falls.
Watch Richard & Adam performing 'The Impossible Dream' on BGT:
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