Cloud computing provides on-demand access to affordable hardware (e.g., multi-core CPUs, GPUs, disks, and networking equipment) and software (e.g., databases, application servers, data processing frameworks, etc.) platforms. Application services hosted on single/multiple cloud provider platforms have diverse characteristics that require extensive monitoring mechanisms to aid in controlling run-time quality of service (e.g., access latency and number of requests being served per second, etc.). To provide essential real-time information for effective and efficient cloud application quality of service (QoS) monitoring, in this paper we propose, develop and validate CLAMS—Cross-Layer Multi-Cloud Application Monitoring-as-a-Service Framework. The proposed framework is capable of: (a) performing QoS monitoring of application components (e.g., database, web server, application server, etc.) that may be deployed across multiple cloud platforms (e.g., Amazon and Azure); and (b) giving visibility into the QoS of individual application component, which is something not supported by current monitoring services and techniques. We conduct experiments on real-world multi-cloud platforms such as Amazon and Azure to empirically evaluate our framework and the results validate that CLAMS efficiently monitors applications running across multiple clouds.