Looking for migration services

[cc1]

A third party service may also do. But they have to be good with no data loss or no uptime issues.

[bsteve]

If you have good host which do provide managed services then they should take care of the migration. If not then go look for another host.

There are few services like you are asking but I will not recommend. Since a third party service is always a bad idea unless you are really big site.

My advice look for good managed service.

And also good customer support along chat.