Amaranthus palmeri is a widespread glyphosate-resistant (GR) weed in the USA. Since 2015, GR populations of A. palmeri have been confirmed in South America, raising the prospect of an ongoing invasion. We used RAD-Seq genotyping to explore genetic differentiation amongst A. palmeri populations from Brazil, Argentina and Uruguay. We also quantified gene copy number amplification of the glyphosate target, 5-enolpyruvyl-3-shikimate phosphate synthase (EPSPS) and the presence of an extra-chromosomal circular DNA (eccDNA) replicon in these populations. Genetic analyses indicated that populations in Brazil, Argentina, and Uruguay were only weakly differentiated (pairwise FST  0.043) in comparison to USA populations. STRUCTURE analysis did, however, assign Argentinean populations to a discrete cluster to those from Brazil and Uruguay. Neither elevated EPSPS copy number, nor the eccDNA EPSPS replicon were present in Argentinean populations, this being consistent with recent observations of other GR mechanisms in Argentina, and an independent in situ evolution of glyphosate resistance. Elevated EPSPS copy number and the EPSPS replicon were identified in all populations from Brazil and Uruguay. The presence of this mechanism and the very high sequence similarity of the EPSPS replicon to that found in the USA are strongly suggestive of the recent invasion of GR into Brazil and Uruguay. Our results are consistent with a single introduction of A. palmeri into South America sometime before the 1980s, and subsequent local evolution of GR in Argentina but with a secondary invasion of GR A. palmeri from the USA into Brazil and Uruguay during the 2010’s.