The Iron Lady star looked visibly shocked when her name was called, and embraced fellow nominee Viola Davis on her way to the stage where she collected her award from last year's 'Best Actor' winner Colin Firth.
As she received a lengthy standing ovation, Streep said: "Oh my God. Oh, come on! Oh, oh! Alright. Thank you so much... When they called my name, I had this feeling I could hear half of America going 'Oh no... Her again!' But, whatever."
Paying tribute to her husband Don Gummer, she continued: "First, I'm gonna thank Don, because when you thank your husband at the end of the speech they play you out with the music, and I want him to know that everything I value most in our lives, you've given me.
"My other partner... 37 years ago... I met the greatest hair and make-up artist, Roy Helland. His first film with me was Sophie's Choice and finally, up until tonight when he won for his beautiful work in The Iron Lady... [we've worked on] every single movie in between.
"I just want to thank Roy - because I really understand I'll never be up here again, but I really want to thank all my colleagues, all my friends."
Streep concluded: "I look out here and I see my life before my eyes. My old friends, my new friends and really... this is such a great honour, but the thing that counts the most with me is the friendships and the love and the sheer joy that we have shared making movies together. Thank you all of you - departed and here - for this inexplicable wonderful career."
Firth also paid tribute to Streep when introducing all the nominees, saying: "Meryl, mamma mia, you are unreasonably good... with every role you play, you raise the bar, making it a little more difficult for the rest of us."
The award is Streep's third Oscar win from 17 nominations across five decades.
More from the 84th Academy Awards
> Oscars 2012: 'The Artist', 'Hugo' win five Academy Awards
> Oscars: Billy Crystal remembers Gil Cates in 'In Memoriam' segment
> Oscars: 'The Artist's Michel Hazanavicius win 'Best Director' gong
> Oscars 2012: 84th Academy Awards live blog
> Oscars 2012: Academy Awards winners list in full
> Oscars: Academy Awards 2012: Red carpet pictures
Watch a trailer for The Iron Lady below: