Davis (pictured), who starts in the role on 7 January, joined the BOA before the London 2012 Olympics and was "custodian of the Team GB brand", Laureus said.
At Laureus, she will oversee the marketing and communications strategy for all elements of the organisation including the World Sports Awards, Sport for Good and the World Sports Academy.
Davis will join ahead of the Laureus World Sports Awards 2019, taking place in Monaco on 18 February.
Jonathan Hill, CEO of Laureus World Sports Awards Limited, said: "We’re delighted to have such an experienced and recognised marketing executive joining the team at a truly exciting point in the growth of our movement. Leah has extensive agency and in-house experience and her knowledge of the current sports marketing space will help us in our goal to take the Laureus story to new audiences around the world."
Davis said: "Laureus is a globally-recognised organisation which uses the power of sport to improve the lives of young people around the world. It’s an honour to join the team at an exciting stage in the journey and I’m excited by the opportunities and challenges that lie ahead. I look forward to working with the team to tell the inspirational stories of the Laureus movement in engaging and innovative ways on a global stage."