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The 28-year-old, second behind Team Sky team-mate Bradley Wiggins in last year's Tour de France, claimed victory after Italian Alessandro de Marchi won the 155.5km eighth and final stage from Sisteron to Risoul.
Froome, Kenyan-born and brought up in South Africa but who has ridden with a British licence since 2008, was followed in the overall standings by Sky team-mate Richie Porte of Australia, who finished 58sec in arrears.
Froome's victory was the third successive British win in the race, Wiggins - who is not defending his Tour de France crown this year - having won it in the past two years.
Froome, who had already been designated as Sky's leader for this year's Tour de France before Wiggins announced he was not going to compete because of injury, had effectively clinched victory in the Criterium with his victory in the first mountain stage on Thursday.
Sunday's stage saw five riders approach the final climb with a lead of more than three minutes and it was de Marchi who was to prove the strongest as he broke free of Belgian Tim Wellens in the final five kilometres.
The 27-year-old Italian came home 24sec ahead of Froome and American Andrew Talansky.
Spain's two-time Tour de France champion Alberto Contador had a miserable stage, falling on the descent from the col de Vars before sacrificing his chances for a consolation stage win by waiting for Australian team-mate Michael Rogers, who was third overall going into Sunday's final stage, when he got into difficulty on the final climb.
Dreadful weather had prompted several retirements during the stage.
Germany's time-trial world champion Tony Martin didn't even start the 155.5km stage from Sisteron to Risoul as he had a sore throat.
Others, though, did start but found the going too tough to see the race through to the finish including French champion Nacer Bouhanni and compatriots Thomas Voeckler, Pierre Rolland and Sylvain Chavanel.
Rolland, eighth in last year's Tour de France, said he had felt a twinge in his Achilles tendon on Saturday evening after the seventh stage.
"We decided with the staff that I would give it a go today but that at the slightest hint of pain I should take no risks with just three weeks to the start of the Tour," he said.
"I am very disappointed and a little and a little crestfallen. I hope that a few days of rest will suffice for me to recover," added the 26-year-old specialist climber.
Others to call it a day were Belgian Thomas de Gendt, Norway's 2010 world road race champion Thor Hushovd and Spaniard David Lopez.
Froome was oblivious to their difficulties as he rode serenely on to record his ninth win of the season, including the Tour of Romandie and the Criterium International.
His only significant defeat came in March in the Tirreno-Adriatico at the hands of Italian ace Vincenzo Nibali, who went on to win the Giro d'Italia
Results from the eighth and final stage of the Criterium du Dauphine from Sisteron to Risoul (155.5km):
1. Alessandro De Marchi (Italy / Cannondale) 4:28:09"
2. Chris Froome (Britain / Team Sky) +24"
3. Andrew Talansky (U.S. / Garmin)
4. Richie Porte (Australia / Team Sky) +31"
5. Jakob Fuglsang (Denmark / Astana) +38"
6. Alejandro Valverde (Spain / Movistar) +49"
7. Joaquim Rodriguez (Spain / Katusha)
8. Daniel Moreno (Spain / Katusha)
9. Daniel Navarro (Spain / Cofidis) +55"
10. Rohan Dennis (Australia / Garmin) +1:00"
Final Classification:
1. Chris Froome (Britain / Team Sky) 29:28:46"
2. Richie Porte (Australia / Team Sky) +58"
3. Daniel Moreno (Spain / Katusha) +2:12"
4. Jakob Fuglsang (Denmark / Astana) +2:18"
5. Daniel Navarro (Spain / Cofidis) +2:20"
6. Michael Rogers (Australia / Saxo - Tinkoff) +3:08"
7. Alejandro Valverde (Spain / Movistar) +3:12"
8. Rohan Dennis (Australia / Garmin) +3:24"
9. Samuel Sanchez (Spain / Euskaltel) +4:25"
10. Alberto Contador (Spain / Saxo - Tinkoff) +4:27"
