The League of Nations was certainly President Wilson's dream (and also the dream of some other world leaders), but it was not the dream of the French, English, Germans, Italians, Russians, or Japanese (to name some names). Although the idea of an international league to preserve peace had circulated in one form or another for over a century, it was Wilson who took up the mantle of an international peace league during the war, and it quickly became the centerpiece of his peace proposal as part of his Fourteen Points (See his Address to a Joint Session of Congress on the Conditions of Peace, 8 January 1918).
The Paris Peace Conference, soon after it got underway, approved a general proposal to create a League of Nation, and after much negotiations, the covenant establishing the League became a major part of the Treaty of Versailles, signed 28 June 1919. After the peace conference concluded, Wilson returned to the US and waged a vigorous public relations campaign to pressure the US Senate into accepting the Treaty of Versailles and the League of Nations. (For his work, Wilson was awarded the Nobel Peace Prize in October 1919) But the Senate refused to ratify the treaty or join the League of Nations, essentially limiting the League's effectiveness. The League held its first council meeting in Paris in January 1920, and then moved and set up its headquarters in Geneva, Switzerland where the first General Assembly was held in November 1920.
Creating the league of Nations (a picture)
Initial Structure of the League of Nations
Websites about the League of Nations