If he is self-employed and he can prove that his self-employment income is guaranteed to continue once in the UK (he will need hard evidence of this), he can just apply using his self-employment income (Category F or G) and won't need to get a new job in the UK first.
However, if he can't guarantee that he will definitely earn at least £18,600 through his self-employment in the UK, he will need that UK job offer of at least £18,600 per year, starting within 3 months of moving back, AND will also need to show he has earned at least £18,600 in the last 12 months in the US.