What about going out for a lunchtime drink with him, just the two of you, and talking about it as a friend. Let him know he's a good worker, but tell him you've noticed the BO problem and that you really want to help him if you can.
If he's already using products and is washing himself and his clothes properly etc., it could be he needs the extra help that his GP could point him to, but that he's to embarrassed to ask about (some people think that they shouldn't be troubling their GPs with 'little' things like this). Offering him support to do this, by encouraging him to seek help and being sympathetic about any time off he might need, will help him to feel more valued as a worker. You never know, if he's not under so much stress, the problem may clear up on its own.
But above all, do let him know that he's performing well in the job - it means the world to some people.