The world-wide ban was the result of a series of UN-negotiated treaties: the Single Convention on Narcotic Drugs (1961), the Convention on Psychotropic Substances (1971) and the United Nations Convention Against Illicit Traffic in Narcotic Drugs and Psychotropic Substances (1988). Local laws such as the US Controlled Substances Act of 1970 were then adopted in response to countries ratifying the treaties.

Prior to that, the Society of Nations had adopted several treaties on the subject. Main focus at the time was on opium.

The main rationale behind the ban was that drugs, particularly addictive drugs, could be a cause of social breakdown and were morally wrong. The driving forces were mostly countries who did not have a tradition of consuming drugs such as opium and did not have an economic stake in the production and sales of these drugs.

Quoting from a 2002 Canadian Senate committee report on drug policy :

William B. McAllister has divided the participating states [in the 1961 conference] into five distinct categories based on their drug control stance and objectives.

• Organic states group: As producers of the organic raw materials for most of the global drug supply, these countries had been the traditional focus of international drug control efforts. They were open to socio-cultural drug use, having lived with it for centuries. While India, Turkey, Pakistan and Burma took the lead, the group also included the coca-producing states of Indonesia and the Andean region of South America, the opium- and cannabis-producing countries of South and Southeast Asia, and the cannabis-producing states in the Horn of Africa. They favoured weak controls because existing restrictions on production and export had directly affected large segments of their domestic population and industry. They supported national control efforts based on local conditions and were wary of strong international control bodies under the UN. Although essentially powerless to fight the prohibition philosophy directly, they effectively forced a compromise by working together to dilute the treaty language with exceptions, loopholes and deferrals. They also sought development aid to compensate for losses caused by strict controls.

• Manufacturing states group: This group included primarily Western industrialized nations, the key players being the U.S., Britain, Canada, Switzerland, the Netherlands, West Germany and Japan. Having no cultural affinity for organic drug use and being faced with the effects that drug abuse was having on their citizens, they advocated very stringent controls on the production of organic raw materials and on illicit trafficking. As the principal manufacturers of synthetic psychotropics, and backed by a determined industry lobby, they forcefully opposed undue restrictions on medical research or the production and distribution of manufactured drugs. They favoured strong supranational control bodies as long as they continued to exercise de facto control over such bodies. Their strategy was essentially to “shift as much of the regulatory burden as possible to the raw-material-producing states while retaining as much of their own freedom as possible.”

• Strict control group: These were essentially non-producing and non-manufacturing states with no direct economic stake in the drug trade. The key members were France, Sweden, Brazil and Nationalist China. Most of the states in this group were culturally opposed to drug use and suffered from abuse problems. They favoured restricting drug use to medical and scientific purposes and were willing to sacrifice a degree of national sovereignty to ensure the effectiveness of supranational control bodies. They were forced to moderate their demands in order to secure the widest possible agreement.

• Weak control group: This group was led by the Soviet Union and often included its allies in Europe, Asia and Africa. They considered drug control a purely internal issue and adamantly opposed any intrusion on national sovereignty, such as independent inspections. With little interest in the drug trade and minimal domestic abuse problems, they refused to give any supranational body excessive power, especially over internal decision-making.

• Neutral group: This was a diverse group including most of the African countries, Central America, sub-Andean South America, Luxembourg and the Vatican. They had no strong interest in the issue apart from ensuring their own access to sufficient drug supplies. Some voted with political blocs, others were willing to trade votes, and others were truly neutral and could go either way on the control issue depending on the persuasive power of the arguments presented. In general, they supported compromise with a view to obtaining the broadest possible agreement.

I would like to add to this question by asking if East Asian governments' strong aversion to narcotics has anything to do with the Opium Wars and their aftermath. From what I understand there are very serious consequences for selling or transporting drugs in Japan, China, South Korea, Singapore, and a lot of other places.