Engineers/Scientists to break into management consulting
I'm afraid I've got to say that many of the things that one might consider an asset, are in reality going to be a hindrance.
Rigour, consistency, reason, domain knowledge, ability to describe uncertainty, always prepared to put appropriate caveats on findings: these are all encumbrances in almost all management consulting.
What you need to cultivate is the ability to form strategy on the basis of a fairly superficial understanding of a business; and the ability to persuade people to pay you lots for you to borrow their watch and then tell them the time.
Oh, and do watch House of Lies through, end to end, a couple of times, to get a feel for it.
Having said that, there is a tiny niche in management consulting available for the skilled technician who's prepared to say no to clients who want "regular" management consulting, and only take on clients who want a thorough, rational, informed job done. There aren't many of those clients, whch is why it's a tiny niche. And it's more likely to be a boutique subject-specific consultancy. But if you find one (or found one, i.e. you are the founder), and it gets the right kind of clients, you'll be very happy (and completely exhausted much of the time), and financially very comfortable while the clients are there.
Your most likely bet is to sell yourself as an operations management specialist. There's an entire field called Industrial Engineering, which is essentially business optimization techniques. There are many aspects of this field that you've likely covered in your coursework, such as optimization methods and probability theory. Emphasizing this in your portfolio can help land you positions in a vast array of fields, ranging from broadly-defined operations management to process engineering to personnel management.
Looking at the current set of responses, they seem to be heavily biased. As someone having spoken to several PhDs in management consulting, let me try to clarify some of the nuances.
First, it is not true that you have to let go of rigor, but rather need to be time-sensitive. This is because the management consulting model works on an hourly-basis and therefore, while consulting on a project, your time determines your payment. Most companies, have several reasons to hire external consultants. At times for the expertise, sometimes for an external perspective, and at other times for helping them communicate capabilities and constraints to their superiors. Regardless, one thing is sure that the time-sensitive nature of the field leads to shorter project life-cycles and at times lack of implementation, which is a stark contrast from a PhD experience where the candidate is the sole worker and implementor.
Second, it is completely false that consulting firms consider PhDs as overqualified. In fact, in top-tier management consulting, advanced degree holders (PhDs) enter at the 'associate' level rather than the 'analyst' level, and generally speaking, move up faster.
Third, and logically following the last point, it is a misconception that consulting firms do not entertain advanced degree holders. In fact, the last I checked, ~10%+ of Mckinsey & Co's total employees were PhDs (as listed on their website). Further, most top management consulting firms have a special set of recruiters meant to be hiring advanced degree holders. You may find them on the company websites.
Finally, I admit that as a field, management consulting has its lows such as those mentioned in the answers thus far, but it would be naive to think that other fields (specially academia) do not have their own shortcomings. Overall, I think that the world needs more PhDs and the management consulting world needs more PhDs working to make corporations better, especially since corporations affect several aspects of our lives.