The Entity Framework provider type 'System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer' could not be loaded

You don't need to Install EF6 NuGet Package in client application, The error is not related to client application because the client application connects to WCF Services and don't know even if a database or data access layer exists.

This error is related to lack of EntityFramework.SqlServer.dll in bin folder of your service library and/or host project.

Option 1

The most simple way is to install EF6 using NuGet Package Manager in your WCF Host project too, and if it has been installed before, try uninstalling and installing it again. This way EntityFramework.SqlServer.dll to output directories.

Please note that this way is somehow against n-layered rules because this your libraries above data access layer are dependent to EF6 which is not so good.

Option 2

As a workaround to copy EntityFramework.SqlServer.dll in output directories, make sure Copy Local of this dll is set to true and then put this code in your DbContext constructor:

var ensureDllIsCopied = System.Data.Entity.SqlServer.SqlProviderServices.Instance; 

It ensures EntityFramework.SqlServer.dll is copied to output directory of consumers of data access project. This is a workaround.

Using this way you don't have any dependency to EF in your layers above data access layer.