Multithreading implementation in threads

I am in process of implementing messages passing from one thread to another

Thread 1: Callback functions are registered with libraries, on callback, functions are invoked and needs to be send to another thread for processing as it takes time.

Thread 2: Thread to check if any messages are available(preferrednas in queue) and process the same.

Is condition_variable usage with mutex a correct approach to start considering thread 2 processing takes time in which multiple other messages can be added by thread 1?