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The seamer, aged 41 years and 348 days, finished with 704 wickets in international cricket.
Having made his debut for England at Lord's in 2003, Anderson will finish his illustrious career at the same ground his 188th Test, two weeks shy of his 42nd birthday.
Kuldeep Yadav became his 700th victim on day three of the contest, when the batter fell caught behind.
20-year-old Bashir will replace Somerset teammate Jack Leach, who hurt his left knee while fielding in Hyderabad, where England grabbed a 1-0 lead in the five-match series.
Moeen Ali, Chris Woakes and Mark Wood come into the playing XI as the hosts look to overturn a 2-0 deficit in the series.
The veteran seamer's fitness will be assessed before next month's Ashes warm-up Test against Ireland.
Anderson dropped to second place after England's stunning loss to New Zealand in the Wellington Test.
Jadeja has moved up to ninth position after his 10-wicket match haul in the second Test against Australia.
Pakistan fought gamely and put on 268 before being all out in the absorbing final session, with Saud Shakeel top-scoring for them with 76.
Anderson, 40, and Broad, 36, were part of the England squad that suffered a 4-0 defeat in Australia in the last Ashes.
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