Based on the description you provided, the combination between the motherboard DZ87KLT-75K and the i7-4770 processor will definitely work.
You can check the processor compatibility list for this motherboard at the following link:
It is also important to mention that the processor i7-4770 is capable to run with a memory speed up to 1600MHz and the memory you have is 2400MHz. However, by default this memory will run at 1333MHz. This means that if you use the memory at 1600 MHz or 1333MHz the processor will work just fine but if you use it higher, it will cause internal problems in the processor.