It's true that Office Web Apps server 2010 is very different from Office Web Apps 2013. OWA 2010 should run on a SharePoint Server and a OWA 2013 should run on stand-alone server(s).
The main reason for this is that other server products (Lync, Exchange and so on) also can use OWA.
For this reason, you should install a new Office Web Apps Server (or Farm actually) that you connect to from your SharePoint Farm.
The tool to use is (as always) PowerShell.
When your Office Web Apps farm is installed and configured, you run several scripts from a SharePoint Server.
# Connect to Office Web Apps Server
New-SPWOPIBinding -ServerName OfficeWebAppsServer -AllowHTTP
# Set to run over HTTP
Set-SPWOPIZone -zone internal-http
# Allow HTTP
$config = (Get-SPSecurityTokenServiceConfig)
$config.AllowOAuthOverHttp = $true
Depending on your security policy, you allow http or https. The default is https.