The Barclays Premier League champions, who lost 3-0 at Manchester City on Sunday, will sign the 21-year-old Ghanaian for an undisclosed fee.
Augsburg confirmed on their official website: "Augs burg and Chelsea have agreed on an immediate transfer of left-back Baba Rahman
Both clubs have agreed not to disclose the fee."
The German club's general manager Stefan Reuter said: "Baba Rahman has developed tremendously in his year with us and made a great leap
It's not just reward for his achievements, but also for our work, if international giants like Chelsea are interested in signing him."
Rahman played 31 games for Augsburg last season after joining from German second division side Greuther Furth.
He said: "I thank all those responsible, the coaches and fans of Augsburg, for their support last year.
"I have to take this chance to play at a top club in England, although I was actually set on a long-term stay in Augsburg a year ago
I felt very comfortable in the team."
Source : PA
Source: PA