The McFly star and professional partner Aliona Vilani received the full seven points from judges for being the last couple standing in the group dance-off.
Chelsee Healey and Pasha Kovalev were runners-up, while Alex Jones and James Jordan finished third.
Jason Donovan, Holly Valance, Anita Dobson and Robbie Savage were previously eliminated by the panel, with last place-finisher Savage receiving just one point.
Explaining the judges' decision, Craig Revel Horwood said that he had been impressed by Judd's "stamina" and "athleticism", which saw him and Vilani continue dancing after they had been announced as winners.
The pair were also praised by host Bruce Forsyth, who said that he had not expected to see such an energetic display by Judd so soon after completing his first dance.
The result meant that Judd and Vilani kept their place atop the leaderboard, having received an almost perfect score of 39 for their earlier quickstep.
The dance was described as "outstanding" by judge Alesha Dixon and Bruno Tonioli called Judd "elegant, sophisticated" and "superb".
The swingathon was introduced to Strictly Come Dancing last year and was won by eventual champion Kara Tointon.
> Strictly Come Dancing Week Nine: In Pictures