Update from moeve (OP): "As of summer 2015 Biber is also included in the 64-bit repositories for MikTeX. There is no need to install Biber manually any more, it can simply be installed via the Package Manager just like other packages."
As Speravir mentioned in a comment to this answer, manually adding files to the MiKTeX directory is not a proper solution to the problem. According to this answer of theirs, it should be avoided for security reasons.
A more secure solution is the one offered here by Bernard, reprinted here:
miktex-biber-bin.tar.lzma from a CTAN repository (direct linked to a mirror near you) and extract the files anywhere on your computer (two steps under Windows). You get a ‘texmf’ directory containing 3 subdirectories (doc, miktex and tpm). You just have to put these 3 subdirectories under the root of your LocalTeXMF directory, and to refresh the FNDB via MiKTeX Options (‘Settings (Admin)’).
If you do not have a LocalTeXMF directory, create one first and declare it via MiKTeX Options, ‘Root’ tab, see Create a local texmf tree in MiKTeX.