Yes, in fact it is likely that your data is safer and more secure than it would be with an on-premise system.
For data in transit, Azure uses industry-standard transport protocols between user devices and Microsoft datacentres, and within the Azure datacentres themselves. For data at rest, Azure offers a wide range of encryption capabilities up to AES-256.
A hybrid solution lets customers decide what gets stored on-premise and what goes to the cloud. Information can be moved back and forth between these options as they see fit. Microsoft takes strong measures to help protect customer data from inappropriate access or use by unauthorised persons, and to prevent customers from gaining access to one another’s data. For more information visit the Microsoft Trust Center
Microsoft solutions and services are built on a trustworthy computing foundation consisting of security, privacy, and reliability. Microsoft creates, implements and continuously improves security aware software development, operational and threat mitigation practices, and shares this knowledge with government and commercial organisations.
Microsoft engages in industry-leading security efforts through its own centres of excellence, including the Microsoft Digital Crimes Unit, Microsoft Cybercrime Center and Microsoft Malware Protection Center. Microsoft continually collaborates with industry and governments to build trust in the cloud ecosystem.