Augsburg have confirmed the deal, believed to be worth around £20million, for the defender on their website.
“Baba Rahman has developed tremendously with us for a year and made a great leap,” said Augsburg commercial manager Stefan Reuter.
“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.”
Baba told the Augsburg website: “I thank all those responsible, coaches and fans of FC Augsburg for their support last year.
“This chance to play at a top club in England is a simple choice, even if I had actually planned on a long-term stay in Augsburg a year ago. I felt very comfortable in the team and will follow them.”