If you are moving to Massachusetts and bringing firearms, you should first obtain the appropriate license and ensure your firearms are legal to possess as previously outlined in this post: I am moving to Massachusetts from another state, do I need a gun license?
Assuming you have obtained the proper license and your firearms are legal to possess under that license, then you are not required to register firearms you brought with you as a new Massachusetts resident under the current statute. The E-FA-10 registry system allows you to register your firearms if you want to, as described further in this previous post: Do guns in Massachusetts need to be registered?
Be careful not to confuse a relocation situation with the requirement to register firearms purchased from an out-of-state dealer. If you are a Massachusetts Resident, and the firearms were directly obtained from an out-of-state dealer, then you would have to register them under this system.
Given the intricacies of Massachusetts firearms laws and the unique legal issues facing firearms owners in the Commonwealth, it is advisable to have an attorney who understands and practices in firearms law, criminal law and civil litigation.