Errors when blog was moved from domain.com/blog/ to anewdomain.com

I had a blog created that was on a separate web host and the URL was something like:

http://www.mysite.com/blog/

And now I am wanting to move it to a separate web host and the URL will be:

http://www.newsite.com/

I backed-up the database and imported the contents into the new hosts remote server and all of the categories and post titles are showing that they are still linked to the old location. How do I fix this? I peeked at the Export .sql file and noticed the wp-option for “home” and it shows the old URL in there… and I’m guessing that thats not the only place that it is going to show up.

Can someone help me on how to fix the database so that the categories and post titles will link correctly to the new domain and new location?

Thank you all in advance!