Multi-cloud is becoming a popular cloud ecosystem because it allows enterprise users to share the workload across multiple cloud service providers to achieve high-quality services with lower operation cost and higher application resilience. In multi-cloud, cloud services are widely distributed at different locations with differentiated prices. Therefore, Web application providers face the challenge to select proper cloud services for application replication and deployment with the aim of minimizing the deployment cost. Meanwhile, the deployed application replicas must satisfy the constraint on request response time to maintain the quality of user experience. To meet the two major requirements, this article studies a new problem of Web application replication and deployment in multi-cloud (WARDMC) that jointly considers both the cost minimization and constraints on average response time, including particularly request processing time and network latency. To address the problem, we develop a new approach named MCApp. MCApp combines iterative mixed integer linear programming with domain-tailored large neighborhood search to optimize both application replicas deployment and user requests dispatching. Extensive experiments using the real-world datasets demonstrate that MCApp significantly outperforms several recently proposed approaches.