Ambrosia artemisiifolia L., (common ragweed), is an annual invasive and highly troublesome plant species originating from North America that has become widespread across Europe. New sets of genomic and expressed sequence tag (EST) based simple sequence repeats (SSRs) markers were developed in this species using three approaches. After validation, 13 genomic SSRs and 13 EST-SSRs were retained and used to characterize the genetic diversity and population genetic structure of Ambrosia artemisiifolia populations from the native (North America) and invasive (Europe) ranges of the species. Analysing the mating system based on maternal families did not reveal any departure from complete allogamy and excess homozygosity was mostly due the presence of null alleles. High genetic diversity and patterns of genetic structure in Europe suggest two main introduction events followed by secondary colonization events. Cross-species transferability of the newly developed markers to other invasive species of the Ambrosia genus was assessed. Sixty-five percent and 75% of markers, respectively, were transferable from A. artemisiifolia to Ambrosia psilostachya and Ambrosia tenuifolia. 40% were transferable to Ambrosia trifida, this latter species being seemingly more phylogenetically distantly related to A. artemisiifolia than the former two.