Red Bull-BORA-hansgrohe's Roglic reclaimed the red jersey from Ben O'Connor with a devastating solo attack on stage 19 on Friday and the Slovenian rider never looked back as he equalled Spaniard Roberto Heras's record of four Vuelta wins.
When Roglic crossed the line, he pointed a finger to the sky and smiled as he finished with an overall lead of two minutes and 36 seconds over O'Connor while Spaniard Enric Mas of Movistar was third.
Victory was all the more special for Roglic who was forced to abandon the Tour de France ahead of stage 13 after the yellow jersey contender crashed twice in consecutive stages.
Roglic, who won three consecutive Vueltas from 2019, came into this year's race as the clear favourite, with Giro d'Italia and Tour de France winner Tadej Pogacar, Jonas Vingegaard and Olympic champion Remco Evenepoel opting not to ride in Spain.
However, he was surprised by O'Connor when the Decathlon-AG2R La Mondiale rider took the red jersey from him on stage six and opened up a gap of nearly five minutes.
But Roglic, nicknamed the 'Slovenian Dream Crusher', slowly clawed his way back and put one hand on the title in stage 19 on the summit finish of Alto de Moncalvillo.
"I expected to be good (at the start of the Vuelta) because I knew I was, but not second overall," O'Connor said.
"Sometimes you've got to trust your gut and other times you could probably be a little bit smarter and not trust your gut as well. So I think it's about picking your moments in grand tours and that's probably the thing I'm taking away."
Roglic was the last rider out for the final stage and the Tokyo Olympics time-trial gold medallist finished with a time of 26 minutes and 59 seconds, good enough for second after Swiss cyclist Kung went 31 seconds faster.
"It's amazing, finally. I've waited, I've been fighting for it for a very long time and I really wanted that win today," Kung said.
"I suffered a lot but I think everyone did at the end of this hard Vuelta ... It's always nice if you win with more than half a minute, it shows you were absolutely the best. It was no coincidence today."