Nitrification, the oxidation of ammonia via nitrite to nitrate, has always been considered to be a two-step process catalysed by chemolithoautotrophic microorganisms oxidizing either ammonia or nitrite. No known nitrifier carries out both steps, although complete nitrification should be energetically advantageous. This functional separation has puzzled microbiologists for a century. Here we report on the discovery and cultivation of a completely nitrifying bacterium from the genus Nitrospira, a globally distributed group of nitrite oxidizers. The genome of this chemolithoautotrophic organism encodes the pathways both for ammonia and nitrite oxidation, which are concomitantly expressed during growth by ammonia oxidation to nitrate. Genes affiliated with the phylogenetically distinct ammonia monooxygenase and hydroxylamine dehydrogenase genes of Nitrospira are present in many environments and were retrieved on Nitrospira-contigs in new metagenomes from engineered systems. These findings fundamentally change our picture of nitrification and point to completely nitrifying Nitrospira as key components of nitrogen-cycling microbial communities.