Tall buttercup, a native of central and northern Europe, has become naturalized in the United States and Canada, and in South Africa, Tasmania and New Zealand. In Canada and New Zealand it has become an economically significant weed in cattle-grazed pastures. In this study we develop a CLIMEX model for tall buttercup and use it to project the weed's potential distribution under current and future climates and in the presence and absence of irrigation. There was close concordance between the model's projection of suitable climate and recorded observations of the species. The projection was highly sensitive to irrigation; the area of potentially suitable land globally increasing by 30% (from 34 to 45 million km2) under current climate when a “top-up” irrigation regime (rainfall topped up 4 mm d−1 on irrigable land), was included in the model. Most of the area that becomes suitable under irrigation is located in central Asia and central North America. By contrast, climate change is projected to have the opposite effect; the potential global distribution diminishing by 18% (from 34 to 28 million km2). This range contraction was the net result of a northward expansion in the northern limit for the species in Canada and the Russian Federation, and a relatively larger increase in the land area becoming unsuitable mainly in central Asia and south eastern United States.