I cannot find any English notices of his death, but there are two German articles in the Die Tagespost:
Klaus Berger gestorben. Der Heidelberger Neutestamentler Klaus Berger ist gestern plötzlich gestorben
Klaus Berger: Gelebte Ganzhingabe. Zum Tod des deutschen Exegeten (Barbara Stühlmeyer)
His brief English Wikipedia page is here. The German Wikipedia page (here) is much fuller. I was mostly familiar with his work on the Aramaic Qumran texts in Die aramäischen Texte vom Toten Meer (Vandenhoeck & Ruprecht, 1984, 1994).
Requiescat in pace.
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