ScottGu announced in his recent post that .NET 4.5 now supported with Windows Azure Web Sites. See detail here.
About .NET Framework 4.5
The .NET Framework 4.5 is a highly compatible, in-place update to the .NET Framework 4. By using the .NET Framework 4.5 together with the C#, Visual Basic, or F# programming language, you can write Windows apps. The .NET Framework 4.5 includes significant language and framework enhancements for C#, Visual Basic, and F# (so that you can more easily write asynchronous code), the blending of control flow in synchronous code, a responsive UI, and web app scalability . The .NET Framework 4.5 adds substantial improvements to other functional areas such as ASP.NET, Managed Extensibility Framework, Windows Communication Foundation, Windows Workflow Foundation, and Windows Identity Foundation. The .NET Framework 4.5 delivers better performance, reliability, and security.
The .NET Framework 4.5 is like a service pack—it's essentially the .NET Framework 4 SP1. It includes bug fixes that do not affect app compatibility and behavior, as you would expect from a service pack. At the same time, we took the opportunity to improve the product, so some .NET Framework 4.5 APIs provide more capability than their .NET Framework 4 counterparts. However, we made sure that .NET Framework 4 apps are not affected by this new behavior, so the experience is the same whether you're using the app or debugging the app in Visual Studio 2012. More info here.
Windows Store apps are designed for specific form factors and leverage the power of the Windows operating system. A subset of the .NET Framework 4.5 is available for building Windows Store apps for Windows by using C# or Visual Basic. This subset is called .NET for Windows Store apps and is discussed in an overview in the Windows Dev Center.
For VS project coexistence and compatibility between VS2010 and 2012, read K. G. Sreeju Nair blog post “Coexistence of projects between Visual Studio 2010 and 2012”.