This biographical and scientific memoir of Dominic Welsh includes summaries of his important contributions to probability and combinatorics. With John Hammersley, he introduced first-passage percolation, and in so doing they formulated and proved the first subadditive ergodic theorem. Welsh has numerous results in matroid theory, and wrote the first monograph on the topic. He worked on computational complexity and particularly the complexity of computing the Tutte polynomial. He was an inspirational teacher and advisor who helped to develop a community of scholars in combinatorics.