Chelsea have completed the signing of the left-back they needed after Baba Rahman joined the club from Augsburg.

After Filipe Luis was sold back to Atletico Madrid, Jose Mourinho was on the lookout for a new fullback, and having zeroed in on the Ghana international, Chelsea finally agreed a fee with Augsburg, believed to be somewhere in the region of €30million (£21m).

Chelsea will pay Augsburg an initial £14m, according to the Daily Mail, with the rest of the fee dependant on appearances and success.

"I am very happy to sign for Chelsea, one of the biggest clubs in the world, and I can't wait to train with my new teammates and very much looking forward to working with them and Mr. Mourinho," Rahman told the club's official website.

"I am also looking forward to having the opportunity to meet the fans as soon as possible."

Rahman will now fight for a place in the playing XI with Cesar Azpilicueta, who has established himself as Chelsea's first-choice left-back under Mourinho.

While the 21-year-old is not expected to usurp Azpilcueta at left-back anytime soon, Rahman could get some playing time if Mourinho decides to play the Spaniard in the other fullback position.

Branislav Ivanovic has struggled at right-back this season, with Jefferson Monteiro and Raheem Sterling giving the experienced defender a hard time. Coping against players with pace is clearly a problem for Ivanovic, and Mourinho might use Azpilicueta as a right-back when up against teams with pace in the wings, with Rahman having plenty of speed to burn.

"It's important because he's a left-back and he can compete with Azpilicueta," Mourinho said after the 3-0 loss to Manchester City, which left Chelsea without a win after two games of the new English Premier League season.

"At the same time, Azpi can also compete with Ivanovic for the right-back position. This player replaces Filipe Luis in terms of the balance of the squad. Hopefully next week he will be ready."