The actress played factory worker-turned-prostitute Fantine in Tom Hooper's adaptation of the classic stage musical Les Misérables.
"It came true," said Hathaway as she looked down at her statue.
"Thank you so much to the Academy for this and for nominating me with Helen Hunt, Jacki Weaver, Amy Adams and Sally Field. I look up to you all so much, and it's just been such an honour. Thank you.
"There are so many people whose generosity and support are the reason I'm standing here right now. I must thank Hugh Jackman. Hugh, you are the best."
She fought back tears as she thanked her other co-stars and team, adding, "Please say I said everyone!" as she continued her list.
"I want to thank my friends, especially the ones who are cheering from Crosby Street tonight," Hathaway continued.
She finally thanked her family and her husband Adam Shulman, saying to him: "By far and away, the greatest moment of my life is the one when you walked into it. I love you so much."
Hathaway concluded: "Here's hoping that someday in the not too distant future, the misfortunes of Fantine will only be found in stories and never in real life. Thank you."
The actress had already been recognised by the BAFTAs, SAGs and Golden Globes, among others, for the role.
The other nominated stars in the category were Amy Adams (The Master), Sally Field (Lincoln), Helen Hunt (The Sessions) and Jacki Weaver (Silver Linings Playbook).
Watch Anne Hathaway as Fantine singing 'I Dreamed A Dream' in a trailer for Les Miserables below:
Oscars 2013 red carpet - photo gallery: