Move from mysite.No-Ip.com to mysite.com

I've been hosting my site from home for a few years now.
I use no-ip's DNS service (I don't have a static IP).
It's come time to move to a web host due to slow speeds (expected from DSL really).
When I move to a pro host I'll no longer need no-ip.com attached to my domain name. The problem is that all links to *.no-ip.com in my site and any site that has links to mine, now become broken.
Someone else out there must have experienced a similar situation.
I'm just wondering what's the best way to deal with this.

 

 

 

 

Top