The Blues have agreed a deal to sign the Ghana international from FC Augsburg and the transfer was confirmed on Sunday night.
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Baba Rahman will replace Luis, who has returned to Atletico Madrid, after only one year at Stamford Bridge.
Mourinho, who watched his Chelsea side lose 3-0 at Manchester City on Sunday, said: “It is important because he is a left-back, so he can compete with [Cesar] Azpilicueta.
“At the same time, Azpilicueta can compete with [Branislav] Ivanovic for the right-back position, so he replaces Filipe Luis in the balance of the squad.”
Rahman was a member of the Black Stars team, that lost in the Africa Cup of Nations final this year to Ivory Coast.