Viner, who becomes the 12th editor and the first woman to run the left-leaning daily in its 194-year history, said it was an "enormous privilege and responsibility".
She will replace Alan Rusbridger, who in 20 years as editor-in-chief has helped transform the paper from a traditional broadsheet to an international digital operation.
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"It will be a home for the most ambitious journalism, ideas and events, setting the agenda and reaching out to readers all around the world."
Since joining The Guardian in 1997, Viner has been a deputy editor, editor of Saturday's edition, deputy women's editor, editor of the G2 supplement and the Weekend magazine.
She launched the newspaper's Australian operation in 2013 and last year became editor-in chief of the four-year-old US digital edition.
Viner hailed the paper's "first-class team of journalists revered around the world for outstanding reporting, independent thinking, incisive analysis and digital innovation".
The Guardian describes itself as "the world's leading liberal voice" and shared a Pulitzer Prize with The Washington Post last year for its reporting on leaks from former National Security Agency contractor Edward Snowden.
Rusbridger was called before the British parliament to counter criticisms that the files created a security risk.
In a statement, he said Viner would bring "immense experience, flair, warmth, imagination and formidable energy to her new role".
The Scott Trust, which owns the Guardian Media Group, chose Viner out of 26 candidates following an indicative ballot of editorial staff, where she emerged the clear favourite.
Outgoing chairwoman Liz Morgan, who will be replaced by Rusbridger early next year following the end of her term, said Viner was an "inspiring and courageous leader".
Viner joins a small group of women at the top of British newspapers, but is the only editor of a major daily title.
She also becomes the first Guardian editor since the 1950s who was not educated at private school.
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