Anders Olsson, chairman of the Nobel Literature Committee, said Fosse's work was rooted "in the language and nature of his Norwegian background".
"I am overwhelmed and grateful," Fosse, 64, said in a statement released by his publishing house, Samlaget.
"I see this as an award to the literature that first and foremost aims to be literature, without other considerations."
One of his country's most-performed dramatists, Fosse has written some 40 plays as well as novels, short stories, children's books, poetry and essays.
The Swedish Academy, which awards the prize, said it was "for his innovative plays and prose which give voice to the unsayable".
Mats Malm, permanent secretary of the academy, reached Fosse by telephone to inform him of the win.
He said the writer was driving in the countryside and promised to drive home carefully.
Fosse is the fourth Norwegian writer to be awarded the Nobel.
Bjornstjerne Bjornson received it in 1903, Knut Hamsun was awarded it in 1920 and Sigrid Undset in 1928.
Fosse's work A New Name: Septology VI-VII - described by Olsson as Fosse's "magnum opus" - was a finalist for the International Booker Prize in 2022.
Anders Olsson, chair of the Nobel Literature Committee, said Fosse's work was rooted "in the language and nature of his Norwegian background".
The Nobel Prizes carry a cash award of 11 million Swedish kronor ($A1.6 million) from a bequest left by their creator, Swedish inventor Alfred Nobel.
Winners also receive an 18-carat gold medal and diploma at the award ceremonies in December.
New laureate Fosse joins an illustrious list of past winners that ranges from Toni Morrison to Ernest Hemingway and Jean-Paul Sartre - who turned down the prize in 1964.
Last year, French author Annie Ernaux won the prize for what the prize-giving Swedish Academy called "the courage and clinical acuity" of books rooted in her small-town background in the Normandy region of northwest France.
Ernaux was just the 17th woman among the 119 Nobel literature laureates.
The literature prize has long faced criticism that it is too focused on European and North American writers, as well as too male-dominated.
In 2018, the award was postponed after sex abuse allegations rocked the Swedish Academy, which names the Nobel Literature Committee, and sparked an exodus of members.
The academy revamped itself but faced more criticism for giving the 2019 award to Austria's Peter Handke, who has been called an apologist for Serbian war crimes.
On Wednesday, the chemistry prize was awarded to Moungi Bawendi of MIT, Louis Brus of Columbia University, and Alexei Ekimov of Nanocrystals Technology Inc.
They were honoured for their work with tiny particles called quantum dots - which can release very bright-coloured light and whose applications in everyday life include electronics and medical imaging.
Earlier this week, Hungarian-American Katalin Karikó and American Drew Weissman won the Nobel Prize in medicine on Monday for discoveries that enabled the creation of mRNA vaccines against COVID-19.
On Tuesday, the physics prize went to French-Swedish physicist Anne L'Huillier, French scientist Pierre Agostini and Hungarian-born Ferenc Krausz for producing the first split-second glimpse into the super-fast world of spinning electrons.
The Nobel Peace Prize is awarded on Friday and the Nobel Memorial Prize in Economic Sciences ends the awards season on Monday.
