Background: Suicide is a major issue for global public health. Suicidality describes a broad clinical spectrum of thoughts and behaviours, some of which are common in the general population. Methods: UK Biobank recruited ~0.5 million middle age individuals from the UK, of whom 157,000 completed an assessment of suicidality. Mutually exclusive groups were assessed in an ordinal genome-wide association study of suicidality: “no suicidality” controls (N=83,557); “thoughts that life was not worth living” (N=21,063); “ever contemplated self-harm” (N=13,038); “an act of deliberate self-harm in the past” (N=2,498); and “a previous suicide attempt” (N=2,666). Linkage of UK Biobank to death certification records identified a small sub-group of “completed suicide” (N=137). Outcomes: We identified three novel genome-wide significant loci for suicidality (on Chromosomes 9, 11 and 13) and moderate-to-strong genetic correlations between suicidality and a range of psychiatric disorders, most notably depression (rg 0.81). Higher polygenic risk scores for suicidality were associated with increased risk of completed suicide relative to controls in an independent sub-group (N=137 vs N=5,330, OR 1.23, 95%CI 1.06 to 1.41, p=0.03). Rs598046-G (chromosome 11) demonstrated a similar effect size and direction (p=0.05) within a Danish suicidality study. Interpretation: These findings have significant implications for our understanding of genetic vulnerability to suicidal thoughts and behaviours. Future work should assess the extent to which polygenic risk scores for suicidality, in combination with non-genetic risk factors, may be useful for stratified approaches to suicide prevention at a population level.