Celtic languages, including Irish, Scottish Gaelic, Welsh and Breton, are today restricted to the Northern European Atlantic seaboard. However, between three and two thousand years before present (BP), Celtic was widely spoken across most of Europe before being largely replaced by Germanic, Latin or Slavic1-4. Despite this rich history, how Celtic spread across the European continent remains contentious5. The debate is currently focused around three main models based on historical linguistics and archaeology: (1) a Late Bronze Age/Early Iron Age spread from Central Europe associated with the Hallstatt and La Tene Cultures6-9; (2) a Late Neolithic/Early Bronze Age spread along the Atlantic seaboard linked to the Bell Beaker Culture10-13; and (3) a Bronze Age spread from France, Iberia or Northern Italy14-16. Previous genomic investigations are centred around the arrival of Celtic to specific regions: Britain17, Iberia18 and Southwestern Germany19. Here, we utilise new genomic data from Bronze and Iron Age Europe to test how the population histories align with the three models of prehistoric spread of the Celtic languages. In line with the theory that Celtic spread from Central Europe during the Late Bronze Age to Early Iron Age, we find Urnfield-related ancestry - specifically linked to the Knoviz subgroup to have formed between 4 and 3.2 kyr BP, and subsequently expanded across much of Western Europe between 3.2 and 2.8 kyr BP. This ancestry further persisted into the Hallstatt Culture of France, Germany and Austria, impacting Britain by 2.8 kyr BP and Iberia by 2.5 kyr BP. Our findings thus agree with the model of Central European spread of the Celtic languages through consecutive expansions of the Urnfield, Hallstatt and La Tene Cultures rather than the competing models. These results demonstrate, yet again, the power of ancient population genomics in addressing long-standing debates in historical linguistics and archaeology.