Team Sky rider Froome had been in second place heading into the 156km-stage from Saint-Gervais Mont Blanc to Modane Valfrejus, some 18 seconds behind American Tejay van Garderen.
Froome, the 2013 Tour de France champion, maintained his momentum from his stage seven triumph to stay with the peloton before attacking on the final climb with 2.6km to go, opening up enough of a margin to secure the overall classification.
The 30-year-old, who crashed out of last year’s showpiece event on the fifth stage, will now look to fine-tune preparations for Le Tour 2015, which begins on 5 July with a time trial in Utrecht.
“The Dauphine was a big focus for me, but the Tour de France is the main objective,” Froome said, quoted on www.teamsky.com.
“The team is ready, and I am almost ready. We are less than three weeks away now and I am really looking forward to it.”
Froome, who claimed his second Criterium du Dauphine title in the space of three years, added: “I couldn’t have expected it to go any better. My legs were really tired after yesterday and the whole team was suffering. I don’t know how they did it but everyone lifted themselves with the yellow and blue jersey in sight.
“They gave everything – Ian Stannard rode alone for almost 100km to control the breakaway and the rest of the team were fantastic up to that moment where I could attack and put pressure on Tejay.”
Lampre rider Rui Costa was third in the overall standings, ahead of Movistar’s Benat Intxausti.
Orica-Green Edge’s Simon Yates claimed the best young rider’s jersey in fifth after the 22-year-old Briton was second on yesterday’s stage.
Defending Tour de France champion Vincenzo Nibali ended in 12th place overall, the Italian Astana rider having faltered on Saturday.