Couples notified the Chairman of the Championship Committee David Pepper and Peter Dawson, Chief Executive of The R&A, on Friday of his plans.
Although Couples has not been a factor at the British Open in recent years, he did finish sixth in 2000 on the Old Course at St. Andrews. When the Open was held at Troon in 1997, Couples tied for seventh.
The 1992 Masters champion has regained some form in the past year, with a win at the 2003 Houston Open that has helped him to the 18th spot in the current Official World Golf Ranking.
Also out of the event are five-time British Open champion Tom Watson, who withdrew because of a shoulder injury, and Fred Funk.
The 133rd Open Championship will be contested from July 15-18 at Royal Troon. Ben Curtis is the defending champion.