Yates (Mitchelton-Scott) was dominant throughout the three-week race across Spain, thriving on the toughest climbs and the flattest routes to secure the victory after the last stage.
Elia Viviani (Quick-Step Floors) won the final sprint for his third stage win in this year's race, with Peter Sagan (BORA-hansgrohe) second and Giacomo Nizzolo (Trek-Segafredo) third.
Yates, 26, successfully defended his lead of one minute 46 seconds over second-placed Enric Mas (Quick-Step Floors). Miguel Angel Lopez (Astana) finished third overall, two minutes four seconds behind, joining Mas and Yates in taking a first podium place at a Grand Tour.
Yates, 26, became the virtual winner of the Vuelta after finishing third in Saturday’s penultimate stage in the mountains of Andorra, making up for his collapse towards the end of the Giro D’Italia after wearing the pink jersey in 13 stages.
He delivered a first Grand Tour victory for the Australian-owned Mitchelton-Scott team and completed a cycle of British victories in the three Grand Tours this year after Chris Froome won the Giro in May and Sky team-mate Geraint Thomas captured the Tour de France in July.
“It feels great. Really unbelievable, I think it’s still sinking in. I have no words, it’s just really unbelievable," Yates said. "I like to race on my instinct and I hope that I continue to do so and achieve more big results like today at the Vuelta a España.
“The day I won on stage 14 is probably my favourite moment from the race, getting your hands in the air, there’s no feeling like winning a bike race and that will hold a special place, but also the first stage in Andorra.
“That was the first day I laid everything on the line to try and win this race and I managed to get a bit of a gap and you start to believe that you may have it, so those two days really stand out for me.
“I came back from real heartbreak from the Giro d’Italia and I am still in shock that I’ve managed to pull it off and it will take a while for it to sink in just what we’ve accomplished. I get really nervous up on the stage, but it was a very special moment that I will cherish forever.”
A late attack from Diego Rubio (Burgos-BH), Joey Rosskopf (BMC) and Nikita Stalnov (Astana) and Garikoitz Bravo (Euskadi-Murias) was controlled by the peloton and held at 15 seconds before the quartet was shut down with seven kilometres to go.
In the final two kilometres there was no clear organisation from the sprint trains, leaving the victory up to the rider with the strongest legs and best timing and for the third time at the 2018 Vuelta that man was Viviani.
"I lost my train today. We’re at the end of the third week of a Grand Tour. That makes a difference. I think I lost my lead out with 2km to go at a roundabout but I remained confident that I’d come from the back," Viviani said.
"At the last corner, I told my guys that I wasn’t there so they slowed down. Every mistake makes us improve. But the outcome is really good.
"We can be proud of what the team achieved during La Vuelta. We also sacrificed our lead-out train in the mountains to give Enric [Mas] the best help to make the podium overall. As a team, we’ve had a beautiful Vuelta."