Migrate Azure database server/database different region
You can use Geo-replication to create a replica of your actual databases on the new desired region, then you can failover all of them making databases on the new region the primary databases, now you can drop all secondary databases on the old original region. You can learn about setting up Geo-replication using Azure portal here.
Another option is to copy the databases to a server located on the desired region using the Copy Database feature as explained here.
A third option is exporting the database to a blob storage as bacpac then import it to a SQL Azure server on the new region as explained here.
Finally, you can also use SQL Data Sync (as explained here) to copy databases to the new region on a new server, and keep the servers synchronized, then you can remove databases from the sync groups, remove SQL Data Sync and drop the original databases.
Hope this helps.