how to inform a direct that he was not chosen for a given new position

I have been on both sides of this interaction. It is not good.
What are you trying to achieve here? Who selected your direct if not you?
I have received employees by my boss's decision. The only professional thing to do in this case is to do everything you can to make them successful. Give them total support, have one-on-ones, give feedback, document all on your sheets. Later, if they do not work out you have the data you need to approach your boss.
The one time my boss told me he did not select me I was too young to know I had better leave. It was a terrible year before he got me fired. He was not being professional but that is irrelevant. I have a standing principle that if my boss doesn't want me on the job I will leave.

I think what you are asking is how to tell a direct that he was passed up for a promotion, correct?
I have had this happen to me a few times.
It is best to give an assessment if what they did well during the interview and where they are professionally lacking in their development.
This helps them to know what to work on before the next promotion opportunity.

One of the best things a manager ever did for me was to sit me down and tell me the truth about my opportunity for promotion within my site.
I am unpromotable where I am now due to perceptions beyond my control. This knowledge has enabled me to reduce my work stress ad concentrate on building my résumé for other companies.
Mac

I'm a fan of being straightforward, so I'd go with the above phrase.  If you're doing this in person, or even over the phone, most people will sense that they're not getting the job through your body language, so they'll be sitting there thinking "JUST GET IT OVER WITH ALREADY" so whatever else you might be saying is just bouncing straight off their forehead.
What you're probably more interested in (or should be), is what else should go into the conversation you have *after* you've said the important bit.  You'll probably have your direct's full and complete attention at this time.  Go over the decision criteria for the job, and identify the areas where your direct did well and where he didn't match up.  DO NOT make comparisons with whoever got the job -- make this all about where YOUR DIRECT is weak.  Describe specific, actionable ways in which your direct can improve his performance in his weak areas.  Offer to engage in MT-style coaching to reinforce those areas and make them strengths.
All of this is, of course, assuming that your direct wasn't chosen for the job simply because there was someone better, and not because you're looking to manage him out.  Also, there is a certain amount of professionalism required on the part of your direct in order to be able to take this analysis objectively and in the manner in which it is intended (assistance to improve) rather than less charitably (justification for why he got shafted).  Only you can decide if your direct is mature enough, and your relationship with him strong enough, to handle this fairly tough talk.