Fellow Briton Stephen Cummings won the final stage from Le-Pont-de-Claix to Superdevoluy, but it was Froome who added to his 2013 and 2015 titles.
The Team Sky rider had opened a 21-second lead heading into stage seven and held out to win by 12 seconds from Frenchman Romain Bardet.
Froome won the Tour de France after both his previous Dauphine successes. This year's edition begins on 2 July.
The 31-year-old had to survive some nervous moments in the final 15km on Sunday, as Spaniard Alberto Contador launched several accelerations on the penultimate climb.
Bardet also tried his chances on a rapid descent between the final two climbs but Froome chased down every attack.
Cummings, 35, was the last of a 20-man breakaway group to wilt and finished well clear of the chasing pack.
Ireland's Dan Martin won the sprint for second with Bardet third, and both moved up a place in the overall standings thanks to the bonus points available on the line.
Tasmanian Richie Porte, who started the day second, was caught out in the uphill sprint finish and lost two places.
Meanwhile, Froome's Team Sky team-mate Geraint Thomas is 17th overall in the Tour de Suisse after finishing three seconds behind stage-two winner Peter Sagan.
Stage seven result:
1. Stephen Cummings (GB/Dimension Data) 4hrs 05mins 06secs
2. Daniel Martin (Ire/Etixx-Quick-Step) +3:58"
3. Romain Bardet (Fra/AG2R) same time
4. Wout Poels (Ned/Team Sky)
5. Adam Yates (GB/Orica)
6. Julian Alaphilippe (Fra/Etixx-Quick-Step)
7. Diego Rosa (Ita/Astana)
8. Louis Meintjes (SA/Lampre)
9. Richie Porte (Aus/BMC Racing) +4:03"
10. Chris Froome (GB/Team Sky) same time
General classification:
1. Chris Froome (GB/Team Sky) 29hrs 59mins 31secs
2. Romain Bardet (Fra/AG2R) +12"
3. Daniel Martin (Ire/Etixx - Quick-Step) +19"
4. Richie Porte (Aus/BMC Racing) +21"
5. Alberto Contador (Spa/Tinkoff) +35"
6. Julian Alaphilippe (Fra/Etixx-Quick-Step) +51"
7. Adam Yates (GB/Orica) +57"
8. Diego Rosa (Ita/Astana) +1:13"
9. Louis Meintjes (SA/Lampre) +1:30"
10. Pierre Rolland (Fra/Cannondale) +2:43"
Britain's Chris Froome won a third Criterium du Dauphine title on Sunday.