The 19-year-old completed his move after his disappointing loan spell at Nottingham Forest was cut short earlier in January.
Santos completed the move while away captaining Brazil's Under-23s at the pre-Olympic qualifying tournament in Venezuela.
Chelsea signed Santos for £16million from Vasco da Gama last January but he is yet to make his debut for the club.
Santos is the second Chelsea player after Angelo Gabriel to join the Alsace club on loan. Strasbourg are owned by BlueCo, Chelsea's parent company run by Todd Boehly and Clearlake Capital, as they build a multi-club model to rival the likes of Manchester City's City Football Group.
Strasbourg are currently 10th in Ligue 1 under former Crystal Palace manager Patrick Vieira.