The site-specific incorporation of bioorthogonal groups via genetic code expansion provides a powerful general strategy for site-specifically labelling proteins with any probe. However, the slow reactivity of the bioorthogonal functional groups that can be encoded genetically limits the utility of this strategy. We demonstrate the genetic encoding of a norbornene amino acid using the pyrrolysyl tRNA synthetase/tRNACUA pair in Escherichia coli and mammalian cells. We developed a series of tetrazine-based probes that exhibit `turn-on' fluorescence on their rapid reaction with norbornenes. We demonstrate that the labelling of an encoded norbornene is specific with respect to the entire soluble E. coli proteome and thousands of times faster than established encodable bioorthogonal reactions. We show explicitly the advantages of this approach over state-of-the-art bioorthogonal reactions for protein labelling in vitro and on mammalian cells, and demonstrate the rapid bioorthogonal site-specific labelling of a protein on the mammalian cell surface.