Accessing EF6 in code throws System.NotSupportedException in EntityFramework.dll - vb.net

Question

based on .NET 4.0 and EF 6.1, I've created a project names Database with an Entity Model to access a SQL Server instance via Designer in Visual Studio 2013.
Additionally, there is an Console Application (also .NET 4.0) trying to consume the entities of the Database-project.
The credentials for the underlying database are stored in the Console Application's App.config within the key <connectionStrings>.
When creating a DbContext in the following way, I can perfectly access the entities:
var db = new MyEntities();
var o1 = db.Buildings.First();
MyEntities is the class that the Entity Framework creates automatically, inheriting from DbContext.
For some compatibility reasons to our guidelines, I'm trying to split up the connectionString into own keys (database, instance, user, password) within Ap.config.
For this, I'm using EntityConnectionStringBuilder to build up the EntityConnection with ProviderConnectionString, Metadata and Provider. It look's like this:
Dim sqlBuilder = New SqlConnectionStringBuilder()
sqlBuilder.MultipleActiveResultSets = True
sqlBuilder.DataSource = "database instance"
sqlBuilder.InitialCatalog = "database"
sqlBuilder.UserID = "user"
sqlBuilder.Password = "password"
Dim providerConnectionString = sqlBuilder.ToString()
Dim metaData = #"res://*/DBModel.csdl|res://*/DBModel.ssdl|res://*/DBModel.msl"
Dim entityConnectionBuilder As New EntityConnectionStringBuilder() With { _
.Metadata = metaData, _
.ProviderConnectionString = providerConnectionString, _
.Provider = "System.Data.SqlClient"}
Dim s = entityConnectionBuilder.ToString()
entityConnection = New EntityConnection(s)
In my Console Application, I call:
var db1 = new MyEntities(entityConnection);
var o2 = db1.Buildings.First();
When executing the last line, the following exception will be thrown:
An unhandled exception of type 'System.NotSupportedException' occurred in EntityFramework.dll
Additional information: Unable to determine the DbProviderFactory type for connection of type 'System.Data.EntityClient.EntityConnection'. Make sure that the ADO.NET provider is installed or registered in the application config.
App.config of Console Application contains the following:
<configuration>
<configSections>
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
<startup>
<supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.0" />
</startup>
<entityFramework>
<defaultConnectionFactory type="System.Data.Entity.Infrastructure.SqlConnectionFactory, EntityFramework" />
<providers>
<provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
</providers>
</entityFramework>
</configuration>
Any ideas, why this exception occurs?