I think the others have good points with regard to the physical work that needs to be done. This client came to you for help, so that is a great first step, and one that I, personally would embrace. Try to build a rapport and make a connection with him–he needs the support and you are a catalyst for helping him make some changes that will lead him to better health.
In addition, I would look at the individual aspects of your question:
If he does not eat well, perhaps you could guide him with a few healthy options or give him some suggestions to make better choices when at work. A little planning on his part could help.
If your client is busy, and we all are, than perhaps you could put together an exercise program that he could manage to fit in on the days that he does not train with you. Make it specific, and give him homework. Let him know that he will see immediate benefits of exercise such as better sleep, reduced stress (a good benefit for him), and more energy. Once he starts seeing changes, this may help his motivation level.
Ultimately, yes, it will be up to him to make these changes and we can only do so much–your client has to be ready to make those changes. But, you are a good influence to get him started down the road to health.