Free Site to Personal Plan (Domain redirect)

I've had a free WordPress site for years, but now I want to buy a Personal upgrade so I can get a custom domain and remove the banner ad. Sadly, I've pasted my free URL all over the internet, which includes the ".wordpress" element, so I think I'll need to redirect, somehow. Or is it the case that buying a plan, which comes with a free custom domain, automatically ensures that the original ".wordpress" URL takes a visitor to the new domain?

Thanks.