Choi, 54, finished with a two-under-par 70 on the final round and ended up with a total of 10-under-par 278 at Carnoustie Golf Links in Scotland. Sunday’s triumph was his first since the 2021 PURE Insurance Championship.
The South Korean rolled in a long putt for an eagle on the par-5 14th to highlight his day. He also had four birdies to offset four bogeys.
Choi entered the final round with a one-stroke lead over Australian Green, who was bidding for his first major on the Champions Tour.
Green shot a 71 on Sunday to finish in second place at eight-under. He shot even-par on the front nine before recording four birdies against three bogeys on the back nine.
The 53-year-old Melburnian ended up two strokes ahead of England’s Paul Broadhurst (70 on Sunday), who won the tournament in 2016 at Carnoustie.
Canadian Stephen Ames, the first-round leader, carded a 71 to reside in fourth place at three-under, one stroke ahead of a seven-golfer contingent for fifth place.
Ireland’s Padraig Harrington, who was included in that mix, had finished second at the event in each of the past two years. He overcame a disastrous start to the final round – a triple bogey and a double bogey on the first two holes – before making a spirited rally to finish with a 72.