The right-back had left Madrid for the Bundesliga side in the summer of 2012 in order to get regular first team action, but the Santiago Bernabeu side opted to exercise their option to re-sign the defender for a set fee after just one year.
"It was an interesting time, one of the most intense in my life, but I took the chance. It was an amazing experience in my development as a player," Carvajal told the official Uefa website.
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"Playing football in a different country was a great opportunity and Leverkusen treated me well. It was wonderful.
"I knew Madrid could sign me again in three years' time, so I worked very hard, but it hadn't crossed my mind that they would come back in for me so soon.
"It was a dream come true when I found out, I was quite emotional. After spending a year away from my family, to get that news was special."
Carvajal, 22, has made 35 appearances in all competitions for Madrid so far this term.