Froome beat four-time Grand Tour winner Vincenzo Nibali by 2min 15sec, with Russia's Ilnur Zakarin completing the podium.
"Thank you so much to everyone who's been a part of this journey," Froome said to the crowds gathered around the Cibeles fountain in the heart of Madrid.
"It's been a whirlwind past three months and so many people have contributed."
The Briton joins Frenchmen Jacques Anquetil (1963) and Bernard Hinault (1978) as the only riders to win the Tour and Vuelta in the same year.
But Froome is the first man to win both races since the Vuelta was moved to after the Tour in the racing calendar in 1995.
Froome, a four-time winner of the Tour de France, had previously finished runner-up at the Vuelta on three occasions in 2011, 2014 and 2016.
The Sky rider led the race all the way from stage three to Madrid thanks to wins on stage nine and the individual time trial on stage 16.
Trentin claimed his fourth stage win of the race on the sprint to the finish line after a 117.6km ride from Arroyomolinos to Madrid, ending in a nine-lap circuit through the center of the Spanish capital.
His victory was Quick-Step's sixth of the race with Yves Lampaert and Julian Alaphilippe also successful.
"I came here to try and win stages, but knowing the parcours didn't allow too many sprints or easy finishes," said Trentin.
"Thanks to the team in three stages of my four we controlled the bunch from the beginning.
"We also won two more stages, so I think we pretty much dominated this Vuelta in stage wins."
However, the Italian was denied the green jersey as winner of the points competition by an insatiable Froome, who sprinted to maintain his lead by finishing 11th on the stage.
"He told me he wanted to defend it and he did," said Trentin.
"With four victories I don't have the jersey, it's kind of a joke.
"It is a pity but I can survive."
There was also an emotional send-off for Alberto Contador on his final day as a professional cyclist.
The three-time Vuelta winner signed off in style with victory on the steep mountain climb to Alto de l'Angliru on Saturday and was given the honor of leading the peloton around the first lap of the Madrid circuit.
"The whole race has been special," said Contador, who also performed a lap of honor before the adoring Spanish crowds.
"Yesterday was as good as it gets. It was a stage I'll always remember and I feel very fortunate."
A winner of seven Grand Tours, Contador is one of just six riders to have won all three of the Tour de France, Giro d'Italia and the Vuelta. — Agence France-Presse
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