Stewart, who is currently the technical director of AS Monaco, will take up the role after completing his commitments with the Ligue 1 side.
He has previously worked with RB Leipzig, Manchester City and the England national team during the 2014 World Cup.
"I am excited to join (Chelsea) to help them build a world-class global sporting organisation to consistently win on the pitch at the highest levels and provide player pathways to help develop our talent," Stewart said in a statement.
Stewart's appointment is the latest development in a major overhaul at Stamford Bridge following the acquisition of Chelsea in May by a group led by Todd Boehly and Clearlake Capital.
"Laurence is an important appointment as we plan to build a deep sporting team that will collaborate closely," Boehly and co-controlling owner Behdad Eghbali said in a joint statement.
"Laurence is a world-class football leader who understands talent management, data and scouting, player development and performance."
Boehly has spoken in the past of his desire to implement a multi-club model at Chelsea. Stewart has prior experience of working in such models, having worked at Leipzig and City, who both have a number of sister clubs across the world.
Chelsea, who are fourth in the league standings, travel to Brighton & Hove Albion on Saturday.
