The American went into the final round of the competition tied for the lead with world number one Rory McIlroy, but shot a round of two-under to secure victory and the £7m cash prize that comes with it.
"I'm on cloud nine. It's unbelievable," Horschel told reporters. "The year I had, I wasn't sure this was going to happen, but I kept believing, everyone on my team kept believing in me and just kept my head up high.
"I'm a positive guy. I always see things glass half-full, and it turned out for the best, and I can't be more thrilled. To cap the year off like this has been pretty unbelievable. I was able to rise to the occasion and get the job done."