Gluck received the award for “her unmistakable poetic voice, that with austere beauty makes individual existence universal,” the Swedish Academy said.
The organization added that she was surprised when she received the phone call that delivered the news of her win to her.
The Nobel Prize in Literature is awarded every year to the person who has “produced in the field of literature the most outstanding work in an ideal direction”.
This is not Gluck’s first high profile award. The American professor of English at Yale University also won the Pulitzer Prize in 1993.
Some of her most famous poetry collections include Averno, which was described as a “masterly collection, a visionary interpretation of the myth of Persephone’s descent into Hell in the captivity of Hades, the god of death”.
Others include The Wild Iris, Meadowlands, Faithful and Virtuous Night among others.
Normally, the Nobel is presented to winners at a formal ceremony in Sweden on 10 December but due to the Coronavirus pandemic, a televised event of winners receiving the prize in their home country will be broadcasted.