According to France Football, the Blues have agreed a deal with his club, St-Etienne, and are confident of completing the move later this week.
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Earlier reports had suggested that the Gunners were leading the race for Souici's signature, but it appears the Chelsea have pipped their London rivals to the France U-16 star.
Premier League Talking Points Round-up - Gameweek 20
Jose Mourinho has offered the 16-year-old a three-year deal, and is confident that Souici will immediately settle into life at Stamford Bridge thanks to the presence of former team-mate Kurt Zouma.
However, a move for Croatia international Andrej Kramaric looks doubtful after Leicester submitted a late bid for the striker, and Mourinho will be keen to complete Souici's transfer as quickly as possible to avoid any repeats.