Who regulates international money transfers globally?

No one regulates international money transfers. Each jurisdiction (originating, transit and termination) have their own financial regulators. For example, if money is being sent from Austin, TX to Manila, Philippines and traverses through a correspondent bank in London, UK, then each city has its own regional regulator. In TX, the Department of Banking (Texas Department of Banking) will be regulating the origination. In London, UK, it would be the FCA, Bank of England and HMRC that would regulate it. In Manila, Philippines, it would be regulated by Bangko Sentral ng Pilipinas (BSP) (the Philippine Central Bank).

Each territory has its own regulator. Then there is the much controversial FATF body (the Financial Action Task Force) an intergovernmental organization founded in 1989 on the initiative of the G7 to develop policies to combat money laundering and is headquartered out of Paris, France. Whilst, FATF issues guidelines that are recommendations - the reality is that if you don’t follow these guidelines, you are expelled from the modern banking system.

Here, for example, is an interactive Map of all US State Regulators that issue the money transmitter licenses for Money Services Businesses: Interactive Map of US State Financial Regulators - Faisal Khan