The Wizards' Council was the predecessor to the Ministry of Magic (FBx). Barberus Bragge was the Chief of the Council in 1269. Burdock Muldoon was Chief of the Wizards' Council in the fourteenth century (FB, QA). He was followed in office by Elfrida Clagg, who is generally regarded as being more enlightened than her predecessors (FB). Elfrida outlawed the hunting of the Golden Snidget, banned its use in Quidditch, and set up a reservation to protect the tiny bird (QA4). The Wizards' Council spent quite a lot of time and effort on trying to figure out who should be allowed to participate in governing the wizarding world. Various definitions were proposed of what constituted a Being and what constituted a Beast. Burdock Muldoon decided that anything or anyone who walked on two legs was a Being, and summoned all Beings to a great coucil to decide on laws. The goblins took advantage of this definition to fill the meeting hall with every strange creature they could find who walked on two legs, from diricawls to pixies to trolls. This disaster led Muldoon to give up trying to integrate non-wizards into the community. Elfrida Clagg, his successor, tried again, this time defining a Being as anyone or anything which could speak in human language. Again, however, this definition brought enormous problems, since creatures such as Jarveys attended and caused mayhem.
The dates of Burdock Muldoon's Chieftainship of the Council are unclear. While his Famous Wizard card gives the dates as 1448-1450, Fantastic Beasts and Where to Find Them indicates that he was Chief in the fourteenth century, not the fifteenth. Elfrida Clagg, according to FB, was Muldoon's successor, but her Famous Wizard card states that she was Chieftainess of the Warlock's Council (sic) during the 1600s.
The International Confederation of Wizards, a governing body overseeing the various individual nations' councils and ministries, met for weeks on end toward the end of the 1600s. Persecution of wizards was growing more and more fierce and something had to be done. The decision was made that the wizarding world would remove itself from contact with the Muggle world. The practcial problems involved in this were tremendous. How do you hide a fully grown dragon, for example? But eventually, in 1692, the Confederation passed the International Code of Wizarding Secrecy. The ministries of every country now subject themselves to this Code, and it is perhaps the most important law in all of the wizarding world. The Confederation still exists today and still maintains the Code of Secrecy, fining nations who fail to keep it carefully (FB) The Confederation met for the first time in France. Its first Supreme Mugwump was Pierre Bonaccord, but the wizarding community from Liechtenstein objected. Bonaccord wanted to give trolls rights and stop the hunting of them, which didn't sit very well with the wizards from Liechtenstein, who were having problems with Mountain trolls (OP31).
The Ministry of Magic, headed by the Minister for Magic, came into being in the late 1600s. The Ministry was involved in the International Confederation of Wizards' decision to create the Code of Secrecy and still today takes the responsibility to enforce the Code. For example, when Harry Potter used a Patronus Charm to drive off two Dementors in the presense of his Muggle cousin, he was nearly expelled from Hogwarts and his wand broken in half as penalty for breaching the Code. The laws against magic-use by underage wizards and against wand use by non-wizard folk are also enforced by the Ministry in part to maintain secrecy. The Ministry evolved over the first half of the 1700s; in 1750, the Department of Magical Games and Sports was created and the Ministries of Magic in every country took full responsibility for the control of the various magical species of plans and animals in their territories.
Associated resources: Ministers for Magic