Cross-disciplinary research (multi-/interdisciplinarity) is incentivized by funding agencies to foster research outcomes addressing complex societal challenges. This study focuses on the link between cross-disciplinary research and its uptake in a broad set of policy-related documents. Using the new policy-oriented database Overton, matched to Scopus, logistic regression was used in assessing this relationship in publications from FP7- and H2020-supported projects. Cross-disciplinary research was captured through two lenses at the paper level, namely from the disciplinary diversity of contributing authors (DDA) and of cited references (DDR). DDA increased the likelihood that publications were cited in policy documents, with DDR possibly making a contribution, but only when publications result from the work of few authors. Citations to publications captured by Overton were found to originate in scientific advice documents, rather than in legislative or executive records. Our approach enables testing in a general way the assumption underlying many funding programs, namely that cross-disciplinary research will increase the policy relevance of research outcomes. Findings suggest that research assessments could benefit from measuring uptake in policy-related literature, following additional characterization of the Overton database; of the science-policy interactions it captures; and of the contribution of these interactions within the larger policymaking process.