Voro Gonzalez has replaced Celades as manager until the end of the season in what is his sixth spell as Valencia’s temporary boss.
He first took over in 2008 after Ronald Koeman’s sacking and helped the La Liga side avoid relegation.
Celades was named Valencia boss in September after Marcelino’s sacking.
He is the sixth manager to be dismissed since Singaporean billionaire Peter Lim bought the club in 2014, while Sanchez – appointed in January – is the sixth sporting director to leave in the same period.
According to reports in Spain, Sanchez resigned shortly after Celades’ sacking on Monday, having earlier told the squad their manager would still be in charge for Wednesday’s game against Athletic Bilbao.
Valencia are eighth in La Liga, and have lost three of their past four games.