BEIJING—To comply with tough new cybersecurity rules, Apple Inc. will begin storing all cloud data for its China customers with a government-owned company—a move that means relinquishing some control over its Chinese data.

Apple will build its first Chinese data center in the southern province of Guizhou to house data for customers of its iCloud service. The data include photos, documents, messages, apps and videos uploaded by Apple users throughout the mainland, the company said Wednesday.

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