What is the likelihood of a PhD admission if a professor agrees to supervise? A very nervous potential PhD student here! 

Long story short, I have been applying to quite a few bioinformatics PhD programs in the US and been rejected from most of them. I did my masters in the UK, and had unfortunately fallen ill during its course and had to take a break so didn't end up doing great. My undergrad GPA is ok (3.12). I did however do good work during my Undergrad and masters, and have a really supporting recommendation letter to show for it.

I had a very promising interview with a professor from a Flagship State University who has agreed to supervise and fund me (Research assistantship). Suffice to say our research interests match a lot and I also think the professor would be a great supervisor. The professor has also been actively following up on my application within the department.

My question here is, what are my chances of getting admitted? 

The department doesn't have a "PhD program" per se (i.e. traditional program where students are admitted and then find a supervisor). Students seem to contact supervisor and find funding through that route and then apply. I am not sure how the application processes work in the US.
Your odds are better than they might be otherwise, but they're not necessarily 100%, either. 

Part of the issue is that some schools may not recognize or honor such "claims" or "gentlemen's agreements" to fund people after they are accepted. More importantly, the issue is that US admissions are typically done at the departmental level, not the faculty member level. That means that a professor telling you that you'll be admitted is not necessarily a guarantee, because the admissions committee has to make that call. (On the other hand, if the advisor in question chairs or is a powerful member of the admissions committee, that changes things substantially!)