The Turkish outfit confirmed the change of leadership after a four-hour meeting of the club's directors on Monday afternoon.
Carvalhal's position had been in jeopardy ever since it emerged that he had fallen out with star player Ricardo Quaresma, although the Portuguese insisted that he had no intention of resigning over the dispute with his compatriot.
However, with Sunday's defeat at home to Samsunspor having left Besiktas fourth in the Super Lig, 20 points adrift of leaders Galatasaray, Carvalhal and the club agreed to part company by "mutual consent", according to a statement on the club's official website.
Carvalhal's successor, Tayfur, spent nine seasons with Besiktas as a player and has been employed in various coaching roles with the club since retiring in 2006.
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