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The 34-year-old beat three-time champion Tony Martin by 26.23 seconds on a hilly 47.1km course in Spain.
After finishing second to Martin in 2011 and 2013, Wiggins finally has a rainbow jersey on the road to go with the six he has won on the track.
"I knew coming into it that I had the legs," Wiggins said afterwards.
"Once I saw the course I realised if I was ever going to beat Tony again it was on a course like this.
"It's been an up and down year - obviously I didn't ride the Tour de France. I want to dedicate this to my family because they had to put up with me when I was at home in July.
"It's my last Road World Championships and I've finished with a gold medal."
Martin trailed Wiggins by 9.64 seconds at the final time-check and the Briton extended his lead in the final 12km.
Wiggins clocked 56 minutes 25.52 seconds to claim a convincing win over Germany's Martin, who was chasing a fourth-successive title. Tom Dumoulin of the Netherlands finished third.
"I knew it would be difficult on the final loop, but I paced it perfectly and still had pace in the final few kilometres," Wiggins explained.
"On my last descent, I heard on the radio that I was 10 seconds up but I pushed all the way to the line because I did not want to take any risks."
Wiggins collapsed to the ground in exhaustion at the finish line but recovered to raise his thumb in celebration when Martin crossed the line.
Victory in north-west Spain gives the 2012 Tour de France winner a world time trial title to go with his three national titles and gold at the London Olympics in the discipline.
"To add the world title is just fantastic. Now I've got the set," added Wiggins.
It is the perfect end to a patchy year on the road and track for Wiggins, who won the Tour of California in May, but then missed out on Team Sky selection for the Tour de France and had to settle for silver in the velodrome in the team pursuit at the Glasgow Commonwealth Games.
His success means he becomes the first British male rider to take world time trial gold since Chris Boardman in the inaugural race in 1994.  Emma Pooley was the last British female to win gold in the event in 2010.
Wiggins has announced that he intends to return to the track for the Rio Olympics in 2016 and also hopes to attempt to break the hour record set by Germany's Jens Voigt last week.
Result:
1.  Bradley Wiggins (GB) 56mins 25.52secs
2.  Tony Martin (Ger) +26secs
3.  Tom Dumoulin (Ned) +41secs
4.  Vasil Kiryienka (Bel) +48secs
5.  Rohan Dennis (Aus) +58secs
Selected other:
20. Alex Dowsett (GB) +2mins 35secs
Great Britain's Sir Bradley Wiggins clinched his first road world title with a thrilling time trial victory at the World Championships in Ponferrada.