You can also change these values through the command line:
shell> mysql DBNAME -u USERNAME -p
mysql> show tables;
(use the table name with _options in the next commands if you changed the table prefix)
mysql> update wp_options set option_value=”NEWPREFIX” where option_name=”siteurl”;
mysql> update wp_options set option_value=”NEWPREFIX” where option_name=”home”;
Just replace NEWPREFIX with the new IP or domain name like “https://new.domain.com/path/to/wordpress”.
I haven’t tried this yet, but I think if you make one blank, the site will get relative URLs instead of prefixing all links with the siteurl.