Can I convert an egg to wheel?

To generate a wheel from an egg, with the Python's wheel package installed, from the command line use:

wheel convert <path-to-egg>

The answer is yes.
We need only wheel package and we don't even need to install it, as according to docs, we can use it directly (due to the fact .whl files have the same format as .zip files and Python can run code in .zip files directly):

pdobrogost@host:~$ python ./wheel-0.22.0-py2.py3-none-any.whl/wheel -h
usage: wheel [-h]

             {keygen,sign,unsign,verify,unpack,install,install-scripts,convert,version,help}
             ...

positional arguments:
  {keygen,sign,unsign,verify,unpack,install,install-scripts,convert,version,help}
                        commands
    keygen              Generate signing key
    sign                Sign wheel
    unsign              Remove RECORD.jws from a wheel by truncating the zip
                        file. RECORD.jws must be at the end of the archive.
                        The zip file must be an ordinary archive, with the
                        compressed files and the directory in the same order,
                        and without any non-zip content after the truncation
                        point.
    verify              Verify a wheel. The signature will be verified for
                        internal consistency ONLY and printed. Wheel's own
                        unpack/install commands verify the manifest against
                        the signature and file contents.
    unpack              Unpack wheel
    install             Install wheels
    install-scripts     Install console_scripts
    convert             Convert egg or wininst to wheel
    version             Print version and exit
    help                Show this help

optional arguments:
  -h, --help            show this help message and exit

Now, all we have to do is to use convert argument and pass egg to be converted:

pdobrogost@host:~$ python ./wheel-0.22.0-py2.py3-none-any.whl/wheel convert ./my-egg.egg

Thanks to Paul Moore for providing answer on virtualenv's group and to Ivo for providing more details on #pip irc channel.