Can I put my Old Hard Drive with the OS in my new PC?

I just bought a barebones PC. My copy of Windows 7 on my current computer is pretty new and I'd rather not have to reinstall it again along with all my software. Can I take the Hard Drive that runs the OS from my old PC and put it in my new PC to run the same copy of the OS? It's Windows 7 Ultimate Retail. Going from a 2.8ghz dual core 4gb ram to 3.2ghz quad core 24gb ram. (I'm a web designer that dabbles in video editing)