On Sunday 16 August, 2015The 21-year-old left-back joins from German Bundesliga club Augsburg.
"Chelsea Football Club is delighted to announce we have reached an agreement with FC Augsburg for the transfer of Abdul Baba Rahman," a statement on Chelsea website read.
Chelsea have completed the signing of Baba Rahman from Augsburg.
The Blues went to the market for a new left-back after selling Filipe Luis back to Atletico Madrid
The 21-year-old, who reportedly passed a medical last week, is believed to have agreed a five-year deal at the Premier League champions.
Rahman, who cost a reported £21.7million, said: "I am very happy to sign for Chelsea, one of the biggest clubs in the world.
"I can't wait to train with my new team-mates and very much looking forward to working with them and Mr (Jose) Mourinho."
Augsburg Commercial Manager Stefan Reuter said on the deal: "Baba Rahman has developed tremendously with us for a year and made a great leap.
"It's not just a reward for his achievements, but also for our work, if international giants like Chelsea are interested in signing him. We wish him well in England."
Mourinho also confirmed the need for Rahman in aiding a struggling defensive unit. "It is important because [Rahman] is a left-back, he can compete with [Cesar Azpilicueta]. At the same time, Azpil can compete with [Branislav] Ivanovic for the right-back position, so he replaces Filipe Luis in the balance of the squad."