Giribet was born in Burgos and grew up in Vilanova i la Geltrú, Catalonia to a legal administrator and an engineer who worked in nuclear power plants. As a boy, he enjoyed windsurfing, beachcombing, and collecting sea shells. He attended, and then graduated from, the University of Barcelona in 1993, with bachelor's degrees in zoology and fundamental biology. He completed his doctorate in animal biology in 1997. He then moved to the American Museum of Natural History for postdoctoral research with Ward Wheeler, and from there moved to Harvard University in 2000, where he went through the ranks until becoming full professor in 2007, Alexander Agassiz Professor of Zoology in 2013, and Harvard College Professor in 2017.
In 2001, with his colleagues from Australian Museum studied the systematics of some Arthropoda species. In 2002, he and Ward Wheeler suggested that the molluscan bivalve group Anomalodesmata should be classless, and that the orders Myoida and Veneroida are not monophyletic. The same year, he, Gregory Edgecombe, and their colleagues studied the phylogenetics of harvestmen, Opiliones, for 18s and 28s genes. Besides the genes, they also discovered that Dyspnoi and Laniatores formed the Dyspnolaniatores superfamily which should be used as new classification for Opiliones. In 2006, he, along with Jon Mallatt, provided evidence that Branchiopoda not Malacostraca is the sister group of Hexapoda after studying ribosomal RNA in various phyla including Kinorhyncha and Ecdysozoa. The same year, he also participated at Harvard Museum of Natural History exhibit where he, Naomi Pierce, Brian D. Farrell, and E. O. Wilson showed species of whip scorpions and Sonoran Desert millipedes. In 2007, he traveled to New Zealand in an attempt to find daddy longlegs spiders but did not find any there. In August 2007, he traveled to Florida, where he proved that harvestmen spiders found there are relatives of the West African ones, because when the supercontinent Pangea broke up the North American part took some of those species with it. In 2009, he discovered the origin and evolution of animal organ systems by studying such bilaterian groups as Acoela and Nemertodermatida, which also proved that Acoelomorpha is not a sister group to them. During the same study he also suggested that the genus Xenoturbella is not a part of Deuterostoma super phylum, and that the genus Symbion and the Deuterostoma actually belong to the Bryzoa and Entoprocta subphyla. In 2009, he and his students traveled to West Africa particularly to Cameroon and Gabon, where they collected velvet worms to compare them to the species found in Central, South America, and the Caribbean.
