The BBC Two documentary-style sitcom beat off competition from Chris Morris's controversial Brass Eye and stage show The Play What I Wrote.
The Office, which is written by and stars Ricky Gervais and is set in a paper merchants in Slough, has won huge plaudits since the start of the first series last year.
The award was presented to Gervais by comedy legend Sir Norman Wisdom.
It caps a memorable rise to fame by Gervais, a former student union entertainment manager who has also managed the band Suede.
PJ Harvey, winner of the 2001 Mercury music prize, was awarded the pop music trophy, despite competition from Irish supergroup U2.
Harvey was unable to attend the ceremony but singer and songwriter Elvis Costello collected the prize on her behalf.
The South Bank Show Awards, held at London's Savoy Hotel on Wednesday, gave trophies to all areas of the arts in th UK, including pop, opera, film and TV.
It is a spin-off from ITV1's long-running arts programme The South Bank Show.
The cinema award went to Last Resort - a love story set among a group of asylum seekers on the south coast of Britain.
It took the title ahead of the gangster movie Sexy Beast and comedy Bridget Jones's Diary.
In literature, author Ian McEwan - whose book missed out on this year's Booker and Whitbread prizes - won best book for Atonement.
There was a special award for Richard Curtis, who created characters such as Mr Bean and Blackadder and who wrote the smash film Notting Hill, which was presented by host Melvyn Bragg.
Awards in full:
Classical music presented by Mitsuko Uchida
Sir Alfred Brendel - 70th Birthday year & Schubert: Piano Sonatas
Pop music presented by Mel B
P J Harvey - Stories From The City, Stories From The Sea
Opera presented by Ian Bostridge
Votzek performed by Birmingham Opera Company
Visual Art presented by Sam Taylor-Wood
Frank Auerbach - Retrospective at Royal Academy
Literature presented by Dame Antoinette Byatt
Atonement by Ian McEwan
Dance presented by Irek Mukhamedov
The Bird Sings With Its Fingers - Mark Baldwin Dance Company
Cinema presented by Michael Gambon
Last Resort
Television drama presented by Michelle Collins
Beckett on Film - Channel 4
Theatre presented by Dame Joan Plowright
This England - The Histories
Comedy presented by Sir Norman Wisdom The Office - BBC Two
Outstanding achievement in the arts presented by Dame Kiri te Kanawa to Bernard Haitink
Special award: 25 Seasons presented by Melvyn Bragg to Richard Curtis