Gittens, 20, was close to making the move prior to the start of the FIFA Club World Cup, but the two clubs could not reach an agreement. Now he has penned a seven-year contract with the English side also participating in the tournament in the USA.
"The negotiations with Chelsea were challenging, but in the end, we are glad that we can realise our expectations and gain planning security," said Dortmund sporting director Sebastian Kehl.
"Jamie is an outstanding player who has given us a lot of enjoyment. He now wants to take the next step in his career at Chelsea, and we wish him all the best and every success."
