This really sucks MS. But fortunately some better programmer than I had the same problem and made this excellent post: http://robsneuron.blogspot.nl/2013/11/entity-framework-upgrade-to-6.html
Adding this line to our DbContext constructor fixes the problem:
var ensureDLLIsCopied = System.Data.Entity.SqlServer.SqlProviderServices.Instance;
The variable is never used, is not needed when using VS to build, it is only there to make sure Ms Build does its job...