You have a CPL. That's what's written on your licence, and that's what the FAA will see when they eventually get the Authority's confirmation.
You need to read FAR 61 and compare the required hours for an FAA CPL with your current experience. Make sure you check the definitions about what counts as x-country and the like.
Presuming you meet the experience requirements you will need to:
* Go through the TSA approval process.
* Do a medical. Cheap & easy.
* Study for, and sit, the CPL theory exam ('knowledge test' in US parlance). You'll need an instructor recommendation ('sign off') to sit the exam but the exam is pretty easy. You can self study for it and no requirement to attend a theory course.
* Do whatever training is needed to pass the CPL flight test ('check ride). Note that what is tested is a bit different to the UK. If you want both single engine & multi engine privileges at Commercial level then that will be *two* checkrides.
* Ditto exam & checkride for the IR