The 'Poker Face' singer took home trophies for International Album, International Breakthrough Act and International Female Solo Artist.
Show host Peter Kay quipped: "She's won every international awards apart from International Male. And that was a close call!"
Accepting her first award, Gaga said: "Thank you so much, I love my fans, thank you so much for everything," before reeling off a list of people who she wanted to thank.
By the time she accepted her third award, for Best International Album, she was in tears.
She said: "I was really excited about winning the first two awards, but this one means more because I worked so hard on this album for so long, and when I think about all that I went through and all the years of struggling and my fans - they were the first ones to recognise my abilities."
Gaga also performed a song at the event - which she dedicated to recently deceased fashion designer Alexander McQueen.
British boyband JLS were the surprise winners of two awards, taking home British Single for their debut 'Beat Again' and British Breakthrough Act. In a triumph for hip hop, 'Bonkers' rapper Dizzee Rascal was named the British Male Solo Artist.
Accepting his award, he thanked his record label, saying: "Whoa, it's about time! Big up to all the Dirtee Stank family, Big up to all the fans!"
Accepting her award in a bright ginger wig, she said: "I wore an orange wig so it would make it harder for the cameramen to find me and see the look of disappointment on my face. But that backfired."
When urged to hurry her speech she replied: "No f**k off, I'm not leaving, f**k off," before thanking her family.
Full list of winners at the BRIT awards 2010:
British Male Solo Artist - Dizzee Rascal
British Female Solo Artist - Lily Allen
British Breakthrough Act - JLS
British Group - Kasabian
British Album - 'Lungs', Florence and the Machine
British Single - 'Beat Again', JLS
BRITs performance of 30 years - 'Wannabe/Who Do You Think You Are', Spice Girls
International Male Solo Artist - Jay-Z
International Female Solo Artist - Lady Gaga
International Breakthrough Act - Lady Gaga
International Album - 'The Fame' Lady Gaga
BRITs Album of 30 Years - 'What's The Story (Morning Glory) - Oasis
Outstanding Contribution to Music - Robbie Williams