It hailed Müller, 56, as a writer who "with the concentration of poetry and the frankness of prose, depicts the landscape of the dispossessed."
Her works are heavily influenced by her time growing up under the totalitarian regime of Romanian dictator Nicolae Ceauşescu.
A spokeswoman for Müller's publisher Hanser Verlag in Munich was ecstatic about the news: "This is fantastic!" She said Müller "laughed and cried" when notified about the award.
"I am stunned and still cannot believe it. I can't say any more right now," Müller said in a statement.
Born in 1953 in a German-speaking enclave in Romania, she emigrated to West Germany in 1987. Her mother spent five years in a work camp in present-day Ukraine and her father served in the Waffen SS during World War II.
In the mid 1970s, Müller studied German and Romanian literature at university in Timişoara, during which time she was linked with Aktionsgruppe Banat, a circle of young German-speaking authors who opposed Ceauşescu's dictatorship.
She later worked at a factory, but was fired after refusing to work as an informant for the secret police.
Müller made her literary debut in 1982 with Niederungen, a collection of short stories, which was censored in Romania. She released an uncensored version in Germany two years later, while at the same time publishing a second book, Drückender Tango, in Romania.
The two works depicted life in a secluded German-speaking village, detailing the corruption and oppression that came with it.
Her most recent work, Atemschaukel (2009), portrayed the exile of German Romanians in the Soviet Union, where many German Romanians were deported at the end of the war.
She currently lives in Berlin, and since 1995 has served as a member of the Germany Academy for Language and Literature (Deutsche Akademie für Sprache und Dichtung).
Her many works are little known outside the German-speaking world, but in Germany, Switzerland and Austria Müller is feted among intellectuals, with the weekly Die Zeit calling her works "an immense literary memo in the history of political terror."
Chancellor Angela Merkel said on Thursday that Müller's winning of the Nobel Literature Prize was a "wonderful sign" two decades after the fall of the Berlin Wall.
"Particularly now, 20 years after the fall of the Wall, this is a wonderful sign," Merkel told reporters. "We are happy that she has found her home in Germany and I congratulate her."
Müller is the 12th woman and the 13th German-speaking author to win the prize.
Germany's Günter Grass was awarded the honour a decade ago and the Austrian playwright Elfriede Jelinek won in 2004.
Grass said on Thursday he was "impressed and very happy" that Müller took the prize this year.
"I'm impressed and very happy because she's a very good writer," Grass told AFP in his native city of Gdansk, northern Poland, where he was opening an exhibition of his graphics Thursday.
"I confess my favourite was Amos Oz. But I must emphasise that the Nobel committee has made a very good decision."
Grass is best known for "The Tin Drum", his first novel set in pre-World War II Danzig - which was renamed Gdansk when it became part of Poland after 1945. It is regarded as a prime sample of European magic realist literature.