The full-back was presented at the Bernabeu on Friday - exactly a year after he was sold to Bayer Leverkusen for 5million euros.
Although he signed a five-year deal with the Bundesliga side last summer, Madrid retained a buy-back clause in the contract, which they exercised last month to bring him back to the Spanish capital for a reported 6.5m euros.
The 21-year old joined Madrid's junior set-up in 2002 before graduating to Real Madrid Castilla, the B team. He spent two years with the reserve side, helping them win promotion to the Segunda Division A, Spain's second tier, in 2011-12, but never made any appearances for the first team.
He will now join the first-team squad for pre-season training on July 15.
"Since I has little, I have worked hard to get here," he said at a press conference.
"I don't want to be an example for anyone, but I want to encourage the youngsters to keep working every day, because making it to the first team is every academy player's dream."
Carvajal believes he is a better footballer after spending a year in Germany and insisted he held no hard feelings with Madrid for sending him abroad.
"We came to a mutual agreement when I left. No-one kicked me out of the club," he said.
"Perhaps if I had stayed I wouldn't be sitting here now. The fact that I am sitting here means that it was the right decision. I was missing a few skills that I needed in order to compete with world-class players and now I've come back to give everything I've got.
"Living alone in another country is a great experience. I made new friends, I matured, and I can tell I have grown a lot."
Carvajal, who will compete with Alvaro Arbeloa for a place in the Madrid starting line-up next season, took time to defend the former Liverpool full-back from criticism following his performance for Spain in their 3-0 defeat to Brazil in the Confederations Cup final.
"I have learned a lot from Alvaro. He is a reference point. He has won two European Championships and a World Cup and he is close to the academy players, which is very important," Carvajal said.
"He is a great player who always gives his all in every game, regardless of the criticism he receives. We'll both try to do our best to make it very hard for the coach to choose who plays."
The defender added that he was looking forward to working under the new Madrid boss Carlo Ancelotti.
"He is a great coach," he said. "Just look at what he has achieved over the years and how many trophies he has won. He treats his players well, forms great groups of players and I'm sure we're going to have a great season."