The Blues have agreed a deal to sign the Ghana international from FC Augsburg and the transfer was confirmed on Sunday night.
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.