SQLite 1.0.91.3 and EntityFramework 6.0.2 in VisualStudio 2013 register sqlite project

Question

I am creating a project with entityframework 5 and SQLite 1.0.91.3 and am creating an entity data model. But after the upgrade object to entityframework 6.0.2, I have an error:

Error 175: the ADO.NET provider with the invariant name "System.Data.SQLite" is either not registered in the machine or application configuration file, or cannot be loaded. See Internal Exception for more details.

How to register System.Data.SQLite?

My configuration:

<configuration>
  <configSections>
    <section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
    <!-- For more information on Entity Framework configuration, visit http://go.microsoft.com/fwlink/?LinkID=237468 -->
  </configSections>
  <connectionStrings>
    <add name="TestDatabaseEntities" connectionString="metadata=res://*/TestModel.csdl|res://*/TestModel.ssdl|res://*/TestModel.msl;provider=System.Data.SQLite;provider connection string=&quot;data source=D:\!Projects\ConsoleAppSQLiteEntity6\TestDatabase.db&quot;" providerName="System.Data.SQLite.EF6" />
  </connectionStrings>
  <startup>
    <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
  </startup>
  <system.data>
    <DbProviderFactories>
      <remove invariant="System.Data.SQLite" />
      <add name="SQLite Data Provider" invariant="System.Data.SQLite" description=".Net Framework Data Provider for SQLite" type="System.Data.SQLite.SQLiteFactory, System.Data.SQLite, Version=1.0.91.3, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
      <remove invariant="System.Data.SQLite.EF6" />
      <add name="SQLite Data Provider (Entity Framework 6)" invariant="System.Data.SQLite.EF6" description=".Net Framework Data Provider for SQLite (Entity Framework 6)" type="System.Data.SQLite.EF6.SQLiteProviderFactory, System.Data.SQLite.EF6, Version=1.0.91.3, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
    </DbProviderFactories>
  </system.data>
  <entityFramework>
    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
      <parameters>
        <parameter value="v11.0" />
      </parameters>
    </defaultConnectionFactory>
    <providers>
      <provider invariantName="System.Data.SQLite.EF6" type="System.Data.SQLite.EF6.SQLiteProviderServices, System.Data.SQLite.EF6, Version=1.0.91.3, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
      <provider invariantName="System.Data.SQLite" type="System.Data.SQLite.EF6.SQLiteProviderServices, System.Data.SQLite.EF6, Version=1.0.91.3, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
    </providers>
  </entityFramework>
</configuration>