The comedian, 55, who described his dance skills as "patchy" when he first signed-up for the BBC One show against younger rivals, triumphed in the final.
And his professional dance partner Oti Mabuse lifted the glitterball for a second consecutive year.
Bailey looked shocked when he was announced as the year's winner and said it felt "surreal... extraordinary" and "wonderful".
The comic, whose performance to Rapper's Delight was one of the stand-out moments of the series, said he could never have imagined getting to the last show.
And he paid tribute to Mabuse, who he called "the most extraordinary teacher, the most extraordinary dancer".
She "believed in me right from the beginning and she found something in me, turned me into this, into a dancer", he said.
Singer and social media star HRVY, EastEnders actress Maisie Smith and reality TV star Jamie Laing were also in the final.
Smith and HRVY would have been Strictly's youngest winners if they had won the public vote.
The nail-biting final began with reference to a "tough day", after Christmas plans were scrapped for millions.
"If ever people needed cheering up, it's now," host Tess Daly told millions of viewers.
"After another tough day, we are going to try our very best to keep you entertained with an unforgettable night of dance."
The BBC's continuity announcer said Strictly had brought viewers together during difficult months.
"In a year that's kept us apart, whether you're watching in Tyne and Wear, Devon, Berkshire or Lincolnshire, we're all watching BBC One together," he said.
Judge Craig Revel Horwood, known for his sharp tongue, referenced the Prime Minister's announcement, following the rapid spread of the new variant coronavirus.
"In light of the recent news, I've decided I'm going to be positive. You may not recognise me," he said.
The Duchess of Cornwall praised Strictly for having "uplifted the nation" when she appeared on the show, in a pre-recorded video clip.
"You have given everybody so much pleasure and you've uplifted the nation," she said.
Culture Secretary Oliver Dowden praised the BBC One series for bringing people together.
"Great reminder of the unique role TV and especially (the) BBC can play in lifting the nation through difficult times," he wrote on Twitter.
"Thank you @bbcstrictly #StrictlyComeDancing".
Co-host Claudia Winkleman fought back tears as she thanked the Strictly behind-the-scenes team who ensured the show returned this year, despite the pandemic, by filming it amid tight restrictions.
"Thank you to the unbelievable Strictly team who managed, against all the odds, to bring us this show in such an unprecedented year... It was a mammoth feat."
Daly thanked viewers "for watching", saying: "We know the show has been a little bit different this year. We are so grateful for your support."
The presenters said the final had attracted an "extraordinary number of votes".
Mabuse also won last year's series, with Kelvin Fletcher.
Her sister, judge Motsi Mabuse, wept as her sibling's name was read out once again.
Bailey takes the record as oldest winner from Joe McFadden, who triumphed in 2017, aged 42.