Besiktas initially promoted Carvalhal from his assistant role when Havutcu was arrested after the club became involved in a last year's match-fixing scandal that threw the domestic league into turmoil.
Havutcu was detained during the probe, in which 93 people including the chairman of champions Fenerbahce, are being tried in an Istanbul court.
Carvalhal remained head coach after Havutcu was released pending trial with eight other suspects in December following the submission of a match-fixing indictment to the court.
Besiktas, currently fourth in the standings - 20 points behind leaders Galatasaray, issued a statement on its website thanking the Portuguese coach for his services to the club.
The team had won only two of its last 11 matches under Carvalhal and was knocked out of the Europa League by Atletico Madrid last month.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.