When he took the stage to accept his award, Ostlund led the crowd in a "scream of happiness" and told photographers to turn their cameras away from him and into the audience.
The film's satire and exploration of moral dilemmas culminated in one of the festival's most eye-catching scenes.
The story centers on a man who is overseeing a new art installation called The Square, a sanctuary where anyone entering it is supposed to abide by humanitarian values - but things quickly go awry. But after he reacts foolishly to the theft of his phone, the respected father of two finds himself dragged into shameful situations.
Kruger dedicated her win to everyone who "has survived an act of terrorism and who is trying to pick up the pieces and go on living after having lost everything".
Joaquin Phoenix was named best actor for his portrayal of a psychologically damaged hitman in "You Were Never Really Here" by British director Scottish director Lynne Ramsay, who shared the prize for best screenplay with the writers of "The Killing of a Sacred Deer", Yorgos Lanthimos and Efthimis Filippou. "This is totally unexpected. you can see from..."
"Un Certain Regard", a separate section from the main contest at Cannes, recognises younger talent and innovative filmmaking. It is scheduled to open in Chicago sometime in June.
The jury also presented a special prize to Nicole Kidman to celebrate the festival's 70th anniversary.More news: ICSE and ISC results will be declared on Monday afternoon
But the I'm So Excited director, known for his interest in female-focused and LGBT storylines, broke down with emotion when asked about 120 Beats Per Minute.
The FIPRESCI critics' jury also rewarded the debut Russian feature "Tesnota" by Kantemir Balagov and Portugal's "A Fabrica de Nada", about workers who take their factory apart rather than let their jobs go overseas, by Pedro Pinho.
Fellow jury member Will Smith was bubbly as ever, saying: "I'm ecstatic".
The Cannes Film Festival Jury has done its job.
The Cannes Film Festival awarded its coveted Palme d'Or award to Ruben Ostlund's "The Square" on Sunday, while Sofia Coppola became only the second woman to win the best director award.
Diane said: "We don't make films for awards".
The Cannes Film Festival is gearing up to award its prestigious Palme d'Or at a glitzy award ceremony.
Fighting back tears, Almodovar told reporters that the "democratic jury" had fiercely debated the winners.
Rasoulof, 45, took best director in the same competition six years ago for "Goodbye" while he was in jail.