Your approach is good. If the new server on the same domain then now issue.
- install the SharePoint on new server( make sure same patch /build level)
- Run the Config wizard on new server and join it to farm.
- if you have any manual changes in SharePoint i.e web.config, please apply on new server.
- Now update your AAM setting(if using the server name and port number)
- Update IIS bindings, and SSL certs( if ssl configured)
- If using DNS, please update them to point new server.
- Start the services on the New Server i.e User profile, MMS, Search etc
- now test everything works as expected
- time to remove the old server from farm.
- Test again.