The Danish international spent the second half of last season on loan at Hamburg, where he made seven Bundesliga appearances, scoring once and providing two assists.
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His performances helped revive his fortunes after a disappointing spell at Genoa and an ultimately unsuccessful stint in Brittany.
Gronbaek joined Rennes from Norwegian side Bodo/Glimt in the summer of 2024 for €15 million but struggled to adapt to French football.
The attacking midfielder managed just 18 appearances for the Rouge et Noir, registering two goals and one assist.
Now permanently settled in Hamburg after what he described as “six excellent months”, Gronbaek will hope to rediscover the form that made him one of Scandinavia’s most highly-rated talents.