We present a framework for verifiable concurrent programming in Java based on a design pattern for concurrency controllers. Using this pattern, a programmer can write concurrency controller classes defining a synchronization policy by specifying a set of guarded commands and without using any of the error-prone synchronization primitives of Java. We present a modular verification approach that exploits the modularity of the proposed pattern, i.e., decoupling of the controller behavior from the threads that use the controller To verify the controller behavior (behavior verification) we use symbolic and infinite state model checking techniques, which enable verification of controllers with parameterized constants, unbounded variables and arbitrary number of user threads. To verify that the threads use a controller in the specified manner (interface verification) we use explicit state model checking techniques, which allow verification of arbitrary thread implementations without any restrictions. We show that the correctness of the user threads can be verified using the concurrency controller interfaces as stubs, which improves the efficiency of the interface verification significantly. We also show that the concurrency controllers can be automatically optimized using the specific notification pattern. We demonstrate the effectiveness of our approach on a Concurrent Editor implementation which consists of 2800 lines of Java code with remote procedure calls and complex synchronization constraints.