Meibom obtained a PhD in physics at the University of Southern Denmark in 1997. He then pursued a two-and-a-half-year postdoc at the Hawaii Institute for Geophysics and Planetology where he studied the mineralogy of primitive chondrotic meteorites. In 2000, he moved to Stanford University as a research associate in the Stanford-USGS ion microprobe laboratory, department of geological and environmental sciences. In 2005, he was appointed as an associate professor at the Museum National d’Histoire Naturelle in Paris, where he was promoted to full professor in 2007. From 2006 to 2011, he served as the director of the French National NanoSIMS analytical facility. In 2012, he was named full professor at the EPFL (École Polytechnique Fédérale de Lausanne) in the School of Architecture, Civil and Environmental Engineering (ENAC). He has also been full professor ad personam at the University of Lausanne since 2014. From 2015 to 2017, he was the director of the Institute of Environmental Engineering at EPFL.
In 2019, Meibom founded the Transnational Red Sea Center (TRSC), an initiative for scientific diplomacy supported by the Swiss Federal Department of Foreign Affairs and which aims to promote scientific collaboration in a politically unstable region endowed with fundamental ecological stakes.