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An, ranked 132 in the world, finished on 21 under par, six shots clear of Spain's Miguel Angel Jimenez (67) and Thailand's Thongchai Jaidee (69).
England's Chris Wood (66) was fourth on 13 under, one shot clear of Italy's Francesco Molinari (74), who was tied for the lead with An overnight.
The 23-year-old An's win is his first on one of the world's major tours.
An was the youngest-ever winner of the US Amateur Championship in 2009, at the age of 17.
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He became only the third European Tour rookie to win the prestigious PGA Championship in its 60-year history and his 267 total over four rounds also beat the tournament record by two shots.
His victory, the first time the European Tour's flagship event has been won by an Asian, will see him climb into the world's top 60, secured his place in the US Open and Open Championship and a five-year exemption in Europe.
"It's going to be life changing," said An, the son of two Olympic table-tennis medallists - his mother Jiao Zhimin represented China and his father Ahn Jae Hyung competed for South Korea.
"This is the biggest event on the European Tour and there are a lot of benefits. I played really well today and had all the confidence going into the last couple of holes."
An began the final round tied for the lead with Molinari and, despite picking up shots at the second and fourth, was only one ahead at the turn thanks to a hat-trick of birdies from Jaidee from the fifth.
However, a birdie at the 11th and tap-in eagle at the 12th gave An a three-shot cushion that became four when Jaidee bogeyed the 13th.
An made certain of victory with birdies on the 15th and 17th and a par on the last completed a hugely impressive performance from the Challenge Tour graduate.
Bristol's Wood had a hole in one at the 14th, winning himself a car from the sponsors in the process.
South Korea's Byeong-hun An carded a final-round, seven-under-par 65 to win the BMW PGA Championship at Wentworth.