The 24-year-old Dutchman joined the Rams from AZ Alkmaar in July 2024 and has since made 48 appearances in all competitions, scoring twice.
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Goudmijn featured 44 times during his first season at Pride Park before making four appearances at the beginning of the following campaign.
He subsequently spent the remainder of last season on loan at Eredivisie side Go Ahead Eagles.
During the 2025/26 campaign, Goudmijn made 23 appearances for the Dutch club, including five in the UEFA Europa League.
He now moves to Zurich-based Grasshoppers in search of regular first-team football. Goudmijn remains contracted to Derby County until the summer of 2028.