The 41-year-old Azinger, who placed seventh in last year's British Open at St. Andrews, is ranked 23rd in the world. He also was runner-up at the 1987 British Open.
Azinger, the 1993 PGA Champion, was diagnosed with lymphoma in his shoulder shortly after his lone major victory, but after chemotherapy and radiation treatment, he was able to make a return to golf.
A native of Holyoke, Massachusetts, Azinger joins fellow Americans Hal Sutton, Lee Janzen, Kirk Triplett and Notah Begay III, who will also not be competing in this year's Open.
The British Open begins on Thursday at Royal Lytham & St. Annes.
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