A professor at Yale University, Gluck, 77, made her debut in 1968 with Firstborn, and is seen as one of the most prominent poets in American contemporary literature.
Her poetry was characterised by “a striving for clarity”, the academy said, with a focus on childhood, family life, and close relationships between parents and siblings.
“In her poems, the self listens for what is left of its dreams and delusions, and nobody can be harder than she in confronting the illusions of the self,” the academy said.
Gluck told The Times she was “completely flabbergasted that they would choose a white American lyric poet”.
“It doesn’t make sense. Now my street is covered with journalists. People keep telling me how humble I am. I’m not humble. But I thought, I come from a country that is not thought fondly of now, and I’m white, and we’ve had all the prizes. So it seemed to be extremely unlikely that I would ever have this particular event to deal with in my life.”
The literature prize has been dogged by controversy in the past several years.
In 2019, the academy exceptionally named two winners after postponing the 2018 prize in the wake of a sexual assault scandal involving the husband of one of its members.
The secretive, 234-year-old academy later announced changes it billed as improving the transparency of the awards process.
But one of the literature laureates announced last year, the Austrian novelist and playwright Peter Handke, had drawn wide international criticism over his portrayal of Serbia as a victim during the 1990s Balkan wars and for attending the funeral of its nationalist strongman leader Slobodan Milosevic.
Milosevic died in detention in 2006 while awaiting trial on genocide charges at the UN war crimes tribunal in The Hague.
The 2016 literature prize granted to American singer-songwriter Bob Dylan sharply divided opinion over whether a popular musician should be given an award that had been largely the domain of novelists and playwrights.
Like much of public life around the world, this year’s awards have taken place under the shadow of the coronavirus pandemic, which led to the cancellation of the splashy Nobel prize-giving ceremony held each December in Stockholm.
Instead, a televised event will be held with winners receiving their honours in their home countries.
This year’s winners will be invited to a ceremony in 2021 to celebrate alongside next year’s laureates, assuming the pandemic has eased by then.
The Nobel prizes are named after dynamite inventor and wealthy businessman Alfred Nobel and have been awarded since 1901 for achievements in science, literature and peace in accordance with his will.
The prizes in medicine, physics and chemistry were awarded earlier this week. The peace prize is to be announced on Friday.