The governance of the Union alternates every two years between the divisions as described in the Memorandum of Cooperation between the two divisions. Currently, the officers are:
- President. Efthymios NICOLAIDIS (Greece; President, DHST)
- Vice President. Menachem MAGIDOR (Israel; President, DLMPST)
- Secretary General. Catherine JAMI (France; Secretary General, DHST)
- Treasurer. Jeffrey HUGHES (United Kingdom; Treasurer, DHST)
- DHST contact for ICSU business. Annette VOGT (Germany)
- DLMPST contact for ICSU business. Benedikt LÖWE (The Netherlands & Germany)
Among the past presidents of the Union were Wilfrid HODGES (DLMPS, United Kingdom, 2010-2011), Liu DUN (DHST, China, 2012-2013), and Elliott SOBER (DLMPS/DLMPST, United States of America, 2014-2015).