The Spanish midfielder moved to Stamford Bridge in the final hours of deadline day, becoming Thomas Tuchel’s third summer signing after Romelu Lukaku and Marcus Bettinelli.
Chelsea are believed to have paid the La Liga champions a loan fee worth around £4.3m and have the option to sign the 26-year-old permanently next summer for around £34.3m.
The London club have confirmed that Saul will wear the number 17 shirt, which he previously sported during his first two seasons at Atletico.
Midfielder Mateo Kovacic, who Saul is set compete with for a place in Tuchel’s starting lineup, was the last Chelsea player to wear the number 17.
The Spaniard could make his Chelsea debut after the international break when the Blues face Aston Villa in the Premier League on September 11.