The club says on Saturday the 30-year-old Hitz signed a contract until 2021.
Hitz takes the place of the retired Roman Weidenfeller, who made his last appearance for the club as a substitute in the final league game of the season against Hoffenheim. Weidenfeller had been with Dortmund since 2002.
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Hitz will compete with compatriot Roman Buerki for the No. 1 slot, finding himself in a similar position to the one he was in at Wolfsburg, where he was usually behind another Swiss goalkeeper, Diego Benaglio.
Hitz spent five seasons at Wolfsburg before leaving in 2013 for Augsburg, where he spent another five years as the No. 1.