The now 36-year-old Russian finished fourth in the triple jump in Osaka but inherited third after the disqualification of Chrysopiyi Devetzi of Greece, also for doping.
The 2007 bronze medal could now go to Slovenian Marija Sestak, who originally finished fifth.
Pystykh's positive result for anabolic steroids at the 2007 world championships was revealed in a retest of samples.
All Pystykh's results from July 6 2013 to her provisional suspension on December 15 2016 have also been wiped from the record books, CAS added, after she failed a second test for an unspecified banned substance.
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