There is no such thing as blanket "international recognition" as it would imply that all countries and all other institutions have somehow validated the qualifications of one university or higher education provider. Internationally, higher education institutions make their own rules about whose qualifications they accept. There are agreements between countries to mutually recognise the quality assurance systems but in the end it comes down to the preference of institutions.
What is possible is that an institution has met the requirements of an accrediting or recognition body in another country or that it has a relationship with another institution or that its qualifications are given some credence because the countries have an agreement.
In our case we are accredited as an international higher education centre by the British Accreditation Council which is the body that accredits private higher education in the UK. This is in addition to our local accreditation and registration. That means we have been assessed and found to offer higher education at the required local and UK standards. This helps our students as a stamp of approval.
All countries have clearing houses to approve international qualifications. In South Africa this work is done by SAQA. If you are presenting a South African qualification overseas the institution or employer will first check with SAQA that the qualification is registered here. They will then compare curriculum and outcomes and ascertain your likelihood of coping in that system. Our graduates have not struggled to move with our qualifications but it takes – for us and everyone else – quite a bit of effort to put the evidence together as each place has their own requirements. Some professions set additional standards. So please always check the detail and don't simply accept a claim that qualifications are internationally recognised – the detail is really important.