He had the luxury of three-putting the final hole, tapping in from six inches to finish at 22-under 262, while compatriot Zach Johnson (64) was second at 21-under.
"I bought my passport and a couple of jackets. I can't wait to get on that plane," Harman told CBS television.
The leading finisher at the tournament who was not already exempt into the British Open qualified to play at Royal Liverpool starting on Thursday, so Harman was the last player to earn a spot on the charter flight that will arrive in Manchester on Monday morning.
The 27-year-old has played in only one major, the 2012 U.S. Open, where he missed the cut.
Harman collected $846,000 for his first PGA Tour victory. Among his other rewards is an invitation to next year's Masters in his home state of Georgia.
He took a one-stroke lead into the final round, and a fine eagle at the par-five second, where he drilled his approach shot to four feet, was a perfect starting tonic, though it took him several more holes to calm down.
"I was aware of what was going on all day but I didn't really start playing well until I put that in the back of my mind," Harman told reporters.
He has always had a knack for the game, but it was not until earlier this year when he stopped emulating his peers that he started to fulfil his potential.
"I made the decision to try to be a better version of myself and see where that took me," he said.
"I've always been a pretty gifted ball-striker. This was really the first week I felt complete command, working the ball both ways.
"This will have a special place in my heart for the remainder of my career."
He says his height (five feet, seven inches) has long provided motivation.
"I've always had a chip on my shoulder. There are times that it feels good to hit it by a guy who's bigger than me.
"I just try to hit the back of the ball as hard as I can."
(Reporting by Andrew Both in Cary, North Carolina. Editing by Gene Cherry)
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