Transferring a site from a subdomain to an entirely new host

Hi everyone,

Not sure exactly where to put this, but hopefully you can make sense of it.

My dilemma

I am building a website from scratch using WordPress.

It is initially being built on an unused domain that I own, which sits as an addon in my bluehost hosting. I need to build it on this domain so that the design can be approved before moving it to the proper domain.

Once the design has been finalised, I need to move the entire site to a brand new domain, which is on an entirely different hosting account.

Is this possible? Can anyone offer a description of how to go about it?

Thanks so much,
Dave