The first steps towards the formation of the IMU were taken in 1919 in Brussels at the Constitutive Assembly of the International Research Council (IRC)*. In accordance with the program approved in Brussels, the IMU was founded during the International Congress of Mathematicians in Strasbourg on September 20, 1920. Under difficult political and partly still unclear circumstances, described in Lehto's book, IMU faded away in the years 1931-1936. As Lehto wrote "For all practical purposes, the IMU ceased to exist in September 1932". In 1933-1936 a commission that studied the foundation of a new IMU failed.
The rebirth of IMU after World War II took some time. In December 1949, a Policy Committee made the decision that a Union Conference would be held in New York. This took place during August 27-29, 1950 and resulted in a draft of Statutes and By-Laws and an Enabling Resolution. In December 1950, the Statutes and By-Laws of the Union had received their final touch. The Enabling Resolution stated that the IMU would be established as soon as ten countries had joined. This happened on September 10, 1951. The IMU was again in official existence with the Danish Academy of Science as its first headquarters. The first ten members of the new IMU, in alphabetic order, were Austria, Denmark, France, Germany, Great Britain, Greece, Italy, Japan, the Netherlands, and Norway. Five more countries joined in 1951: Australia, Canada, Finland, Peru, and the United States. The first General Assembly took place in Rome in March 1952. The years 1950-1952 are milestones in the history of IMU. The Constitutive Convention in 1950 in New York created IMU de facto. By the Statutes adopted there, IMU came into being in 1951 de jure, and in 1952 the General Assembly inaugurated the activities of the new Union, elected its first President and Executive Committee and was readmitted to ICSU.
To preserve its history, the International Mathematical Union maintains an archive containing important correspondence and documents. The archive keeps, in particular, the correspondence of all IMU Prize selection committees. The IMU Executive Committee decided that all material related to IMU Prizes must be kept confidential for 50 years, though. The IMU archive has been at ETH Zürich for a long period of time until it moved to the University of Helsinki in 1994. In the beginning of 2011 the IMU archive was moved to the new permanent IMU Secretariat in Berlin.
The IMU EC has appointed Prof. Guillermo Curbera (Universidad de Sevilla, Spain, curbera(at)us.es) as "Curator of the IMU archive" for the period 2007-2014. His task is to collect the relevant material, select the documents that should be maintained and keep the archive up to date. Since the beginning of 2011, Guillermo is supported by the IMU archivist Birgit Seeliger (archive(at)mathunion.org) who is in charge of the organization and long-term maintenance of the archive. Persons interested and willing to work in the IMU archive in Berlin are requested to contact Guillermo Curbera (preferably by e-mail) and/or Birgit Seeliger before travelling to Berlin in order to prepare the visit in a best possible way.
Professor Olli Lehto, former Secretary of IMU from 1983 to 1990, has written the book "Mathematics without borders" (a 97 MB pdf file), a history of the International Mathematical Union, published by Springer in 1998. This book is warmly recommended to those interested in the history of IMU. In IMU Bulletin 39, 1995, Olli Lehto gives a short overview about IMU - past and present.
The book "International Mathematical Congresses An Illustrated History 1893-1986" (a 33 MB pdf file) by A. J. Albers, G. L. Anderson, C. Reid informes about the International Congresses of Mathematicians. A fresh look at this history is provided by Mathematicians of the World, Unite! The International Congress of Mathematicians — A Human Endeavor by Guillermo P. Curbera.
The Web page "Historic IMU/ICM Digital Material: Proceedings, Videos, Books" provides a lot of IMU/ICM documents electronically, all free of charge.
*The IRC was disbanded in 1931 and replaced by the International Council of Scientific Unions (ICSU), today called International Council for Science.