You don't say where you are based, but, as part of your Aerodrome course you will be taught about ICAO and ATC licensing.
Basically, it's the CAA of the country where you passed your exams and work which issues your licence, if you choose to work elsewhere you have to meet the requirements of that particular state.
In most cases you will have to undertake an assessment for prior competence to prove that you are capable of working as an ATCO within any particular country.
Some countries accept the ICAO ATCO licence as a standard, others, particularly some western European ones require you to, quite rightly, undergo rigerous assessments before you'll even be considered for acceptance.