The BBC and RTÉ show, starring creator Brendan O’Carroll as foul-mouthed Irish matriarch Agnes Brown, attracts millions of viewers and has spawned a successful movie — despite being dismissed by critics.
O’Carroll deemed the result of the poll “breathtaking...”
“Lost for words... and that doesn’t happen to me very often,” said O’Carroll, whose wife Jennifer Gibney also stars in the sitcom.
“Myself and Jenny are dancing around the living room. I can die happy now... but I’ll take my time...”
A live episode last month attracted 8.82m viewers but Mrs Brown’s Boys has struggled to win over critics.
O’Carroll said of the result: “It vindicates the fans’ belief in the show. They have kept us on the air — it certainly wasn’t the reviewers.”
He told Radio Times magazine, which carried out the poll, that much of today’s comedy output had left behind many viewers.
“There is an audience out there that comedy forgot — that Are You Being Served? audience has been left behind. Us winning this award proves that.”
The Office, created by Ricky Gervais and Stephen Merchant, is second in the poll.
Peter Kay’s Car Share, the comic’s TV comeback last year, is third, above another of his shows, Peter Kay’s Phoenix Nights, in 16th place.
The top 10 also features Count Arthur Strong, which transferred Steve Delaney’s cult Radio 4 hit to TV, in fourth place, followed by Channel 4 sitcom The IT Crowd and Armando Iannucci’s political satire The Thick Of It.
James Corden and Ruth Jones’s hit Gavin & Stacey is seventh, followed by Miranda Hart’s sitcom Miranda, and Raised By Wolves by Caitlin Moran, which was recently axed by Channel 4 after its second series.
Outnumbered, the BBC hit about family life starring Hugh Dennis and Claire Skinner, is tenth.
Benidorm is 19th, the only sitcom from ITV in the poll cast from 14,000 votes from a shortlist compiled by Radio Times critics and experts from the British Film Institute.