Clarke managed to overcome a late rally from Ireland's Padraig Harrington on Sunday by sinking the birdie to polish off a one-under par 69 and finish on 10-under 270 for the week.
Harrington birdied six holes on the back nine to shoot a 67 and set the clubhouse pace at nine-under before Clarke's finish.
After his second shot landed just shy of the 18th green, Clarke nailed a perfect lag putt from the fairway that nestled within a few feet of the back pin location, allowing him to tap in for the title.
Not only did the 53-year-old win his first senior major championship, but he also became just the fourth player in history to win both the British Open and the Senior Open, joining Gary Player, Tom Watson and Bob Charles.
Clarke, who won The Open in 2011 at Royal St. George's, also prevented Harrington, the two-time British Open champ, achieving the equivalent feat.
Heavy rain interrupted the end of Sunday's round, with a two-hour delay ending at 8pm local time.
Before the delay, Clarke had opened his round with nine straight pars and a bogey at the par-five 10th before birdieing the par-four 12th for a one-stroke lead.
Harrington, 50, who won last month's US Senior Open on his debut, had a rough start with a bogey at the seventh and a double bogey at the ninth.
But he made birdie at No.10 to kick-start a red-hot back nine that wasn't tempered by the rain delay.
His birdie-birdie finish wrapped up a 30 on the back nine and put himself in front before Clarke won it on the final green.
Clarke had led after two rounds and shared the 54-hole lead with England's Paul Broadhurst, the 2016 champion.
Broadhurst shot a one-over 71 and was one of six players to tie for third at eight under, joining Argentina's Mauricio Molina (65), American Doug Barron (65), South African Ernie Els (68), Thailand's Thongchai Jaidee (68) and New Zealander Steven Alker (70).
The leading Australian was Stuart Appleby, who finished 19th on two under after a final round 74, one shot ahead of his 20th-placed compatriot Peter O'Malley.
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