Fitzpatrick, who won the 2013 U.S. Amateur, is ranked 41st. An, who won the 2009 U.S. Amateur, is ranked 56.
Others earning exemptions included Spain's Jon Rahm and Rafael Cabrera Bello, England's Ross Fisher and Lee Westwood, Austrian Bernd Wiesberger, South African Louis Oosthuizen, Belgian Thomas Pieters, Swede Alex Noren, Japan's Yuta Ikeda and Hideto Tanihara, Canadian Adam Hadwin, South Korean Wang Jeung-hun, Italian Francesco Molinari and Australian Marc Leishman.
Billy Horschel was among a group of Americans also claiming exemptions after moving into the top 60 by winning the AT&T Byron Nelson on Sunday in a playoff against Jason Day.
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The winner of the May 25-28 European Tour BMW PGA Championship will also earn an exemption.
The number of fully exempt golfers may increase with the addition of others who move into the top 60 players from the rankings as of June 12. Other spots in the field will be filled through sectional qualifiers.
(Reporting by Larry Fine in New York; Editing by Ken Ferris)
