The Santiago Bernabeu side spent €25 million to lure the Germany international to La Liga while splashing out €80m on the Colombia star, with both players earning 16th and 6th place respectively in the 2013-14 Goal 50 list for their impressive form over the past year.
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"James is going to bring a lot to the team and will make us players and the club even better," the defender said at a press conference.
"As a team-mate I wish him all the best and I'm certain he'll do well.
"Kroos is a fantastic player. I had to deal with playing against him in the Bundesliga and I faced him this year in the Champions League semi-finals.
"He will bring a lot to the centre of midfield."
Carvajal went on to stress he is happy to fight it out with Alvaro Arbeloa for the position of right-back after head coach Carlo Ancelotti rotated the two in 2013-14.
"The rotation system was good for both of us and the team last season," he added.
"We will be fighting to get as much playing time as possible because playing for a team as important as Real Madrid is a big deal."