The Conservative life peer, who helped to found the Centre for Social Justice with Iain Duncan Smith and worked with him at the Department for Work and Pensions, will join the group to "lead its mission to promote the ideas and policies that help individuals flourish and nations prosper".
The Legatum Institute is known for its annual prosperity index, which ranks countries across the world on both their national wealth and the wellbeing of citizens, combining indicators such as GDP, personal freedom, education systems and healthcare.
Stroud, who will take up the role on 31 October, said: "I am honoured and excited to be appointed chief executive of the Legatum Institute. We share a passion to help each person, family, community and nation reach their full potential."
Chairman of the Legatum Institute Alan McCormick added: "Philippa has committed her life to social reform at both the local and national level. She shares our vision that personal transformation is possible and that through careful research and data, it is possible to understand what drives and constrains the creation of lasting prosperity and wellbeing."