The 45-year-old will act as the club's coach on an interim basis, until Tayfur Havutcu's legal problems are solved
The Portuguese tactician will guide the club until the Turkish justice rules on the case of Tayfur Havutcu, who is being investigated for his alleged involvement in a match-fixing scandal.
Besiktas unanimously decided that Havutcu and his assistants would remain with the club following a board meeting on Tuesday morning.
Besiktas, who finished fifth in the league last season, allegedly tried to fix the Turkish Cup final, which they won against Istanbul Buyuksehir Belediyespor 4-3 on penalties in May.
Carvalhal, 45, was last seen coaching Sporting Lisbon in the 2009-10 season, replacing Paulo Bento, who is now at the helm of the Portugal national team.
As originally intended, he left Sporting at the end of the campaign, having guided the club to a fourth-placed finish in the league.