Fredrik Andersson (69), Brian Davis (68) and Andrew Marshall (70) shared second place at 8-under-par 280.
Dredge tied the European Tour record with a 60 on Saturday, but that mark will not go into the record books because the players were playing preferred lies. He was never threatened on Sunday despite bogeying the first hole.
'It feels wonderful,' said Dredge. 'I have waited a long time for this so I will savour it for a few weeks. Going out in the third round and shooting 60 made it so much easier for me and although I made a few errors I knew my game was in good shape.'
He erased his early mistake with a birdie at the par-5 third. He had a lot of success on the par-5s this week, going 11-under-par on the four par-5s on the course.
Dredge, whose best career finish prior to this was a tie for second at the 2002 European Open, notched his second birdie of the day at the par-5 seventh, but dropped a shot with a bogey at the next.
Dredge birdied the par-5 11th and the par-4 13th around the turn. He carded four straight pars before bogeying the last for a final-round 71.
'When I was asked if I had thought about holing a winning putt when I was a 15-year-old I never imagined it would be from four inches and having about eight putts from there,' said Dredge.
Andersson mixed four birdies and one bogey into his final-round 69.
'I can't say I played perfectly but I holed enough putts and scored well which is the main thing,' said Andersson. 'There was no chance of catching Bradley after his round yesterday so to finish second is good.'
Davis joined Andersson in second with five birdies and one bogey for a 68 on Sunday. They were joined in second place by Marshall, who had four birdies and a pair of bogeys in the final round. This was Marshall's best career finish on the European Tour.
Sam Little finished alone in fifth place at 7-under-par 281. Robert-Jan Derksen was one stroke further back at minus-6. Santiago Luna, who won this event in 1995, ended in seventh place at 5-under-par 283.
First and second-round leader Jesus Maria Arruti shot a final-round 71 to tie for 11th at 3-under-par 285.