Perinatal factors have been associated with soft tissue sarcomas (STS) in case-control studies. However, (i) the contributions of factors including fetal growth remain unknown, (ii) these factors have not been examined in cohort studies and (iii) few assessments have evaluated risk in specific STS subtypes. We sought to identify the role of perinatal and familial factors on the risk of STS in a large population-based birth cohort. We identified 4,023,436 individuals in the Swedish Birth Registry born during 1973-2012. Subjects were linked to the Swedish Cancer Registry, where incident STS cases were identified. We evaluated perinatal and familial factors obtained from Statistics Sweden, including fetal growth, gestational age, and presence of a congenital malformation. Poisson regression was used to estimate incidence rate ratios (IRRs) and 95% confidence intervals (CIs) for associations between perinatal factors and STS overall, as well as by common subtypes. There were 673 individuals diagnosed with STS in 77.5 million person-years of follow-up. Having a congenital malformation was associated with STS (IRR = 1.70, 95% CI: 1.23-2.35). This association was stronger (IRR = 2.90, 95% CI: 1.25-6.71) in recent years (2000-2012). Low fetal growth was also associated with STS during the same time period (IRR = 1.86, 95% CI: 1.05-3.29). Being born preterm was associated with rhabdomyosarcoma (IRR = 1.74, 95% CI: 1.08-2.79). In our cohort study, those with congenital malformations and other adverse birth outcomes were more likely to develop a STS compared to their unaffected contemporaries. These associations may point to disrupted developmental pathways and genetic factors influencing the risk of STS.