Warren and Dredge were tied atop the leaderboard overnight but Warren surged ahead of the Welshman with three birdies on his first eight holes to open up a four-shot lead. Warren made two more birdies coming home and could afford his second bogey on the day on the 18th hole for a 9-under 275 total.
It was Warren's first title since winning the 2007 Johnnie Walker Championship, after several recent near misses.
''It feels incredible,'' Warren said. ''Today I kept telling myself I was swinging the club really well and I was confident in what I was doing.''
Dredge finished with a 70 after mixing six birdies with five bogeys, ending with a 7-under 277 total.
Warren and Dredge were well clear of the rest, with England's Phillip Archer (69) finishing third with an overall 4-under 280.
More than 80,000 fans watched during the four days at Himmerland Golf & Spa Resort, at times braving gusty winds and rain.
''The crowds have been amazing,'' Warren said. ''Coming down those last four holes, the crowds were so big.''
On Sunday, play was delayed about 90 minutes by rain but Warren took advantage of the slightly lighter winds at the first European Tour event in Denmark since 2003.
Denmark's Thomas Bjorn was tied for fourth on 3-under 281 alongside Englishmen Oliver Fisher and Eddie Pepperell. All three shot 69 on Sunday.