The other writers are Neel Mukherjee, Ali Smith, Joshua Ferris, Karen Joy Fowler and Richard Flanagan.
It is the first year the prize has included US writers, having previously included those from the Commonwealth, Ireland and Zimbabwe.
The winner of the £50,000 prize will be announced on 14 October.
The shortlisted authors each receive £2,500 and a specially bound edition of their book.
AC Grayling, the chair of the judges, said they “just chose the books which were the best”, adding “there was no question of tokenism”.
“As the Man Booker Prize expands its borders, these six exceptional books take the reader on journeys around the world, between the UK, New York, Thailand, Italy, Calcutta and times past, present and future,” he said.
Judge Sarah Churchwell said the books carried modern themes, adding: “These novels are very engaged with the contemporary world.
“It is striking when we look at the books selected in the recent past how strong historical fiction was. Although we got many wonderful historical novels we felt with these six, that there were some very interesting books here about the 20th and 21st Century.”
She later added that Smith’s novel does feature the Renaissance era, but from a modern perspective.
Previous winners of the prize have included Hilary Mantel, whose 2012 winner Bringing up the Bodies, was about Thomas Cromwell, an adviser to King Henry VIII, and charted the bloody downfall of Anne Boleyn. It was the sequel to Wolf Hall, which won the prize in 2009.
The judges say they were interested only in the quality of the writing, but in the end they have come up with a shortlist that ticks all the boxes. Neat and tidy, some might even say rather safe.
Two women make the final six. And fears the prize would be swamped by American writers have proved unfounded. Only two authors from the United States make the final list. Joshua Ferris, whose book was dubbed “The Catch-22 of dentistry” by Stephen King and Karen Joy Fowler’s family saga which has already won the 2014 PEN/Faulkner Award for Fiction.
In recent years historical fiction has dominated the prize, so it is notable that this year the books are set in the future, present or recent past. Art, war and the internet emerge as key subjects. But traditional themes are still at the forefront: love and grief, ambition and desire and the strangeness of the ordinary.
The judges said it was “really difficult” to come up with the shortlist. They say that every year. But it did take them three hours and 40 minutes to reach a decision, which is longer than usual. I suspect some books passed smoothly from longlist to shortlist, but others were argued over far more vociferously.
for We Are All Completely Beside Ourselves, about an ordinary Mid-western family: two parents and three children – one of whom turns out to be surprisingly special.
“I’ve been given opportunities to travel and to see my book read by such an astonishingly wide readership all over the world,” she said.
This year’s ceremony will be broadcast by the BBC.