Joining Real Madrid marks the fulfilment of a childhood dream for Thibaut Courtois – who won La Liga with bitter rivals Atletico in 2013-14.
Courtois completed his long-mooted switch from Chelsea to the European champions on a six-year deal and was presented at the Santiago Bernabeu on Friday.
The 26-year-old Belgium international penned his six-year contract before an audience that included his two children, both of whom live in the Spanish capital with his former partner.
"Today I fulfil a dream," Courtois said. "You cannot understand how happy I am. Those who know me know the effort I have put in to get here.
"My hard work and my feelings have always been about being the best. I have the chance to fulfil a new dream.
"I have dreamt about this since I was a child, admiring those who came on to the pitch to represent Real Madrid.
"I have been a rival and I know what it is to face Real Madrid. Today I'm one of you. Hala Madrid."
Madrid president Florentino Perez lauded Courtois' performances, which helped Belgium to finish third at the 2018 FIFA World Cup, before acknowledging the family ties that proved a key factor in the transfer.
"Today is another happy day for Madridistas because we have another excellent player joining us," said Perez.
"Real Madrid will look to keep this incredible period of success going, faithful to our history. Our strategy is to make a team with the best players in the world, the best players in Spain and a youth academy that has always been our identity.
"It's a great day, we've got an important player who will help us to be better. The best goalkeeper from the last World Cup. Welcome, Thibaut Courtois. One of the best goalkeepers in the world, if not the best.
"Everyone knows Thibaut was vital in Belgium coming third. The signing of Courtois is part of our strategy of the club as well – to bring in players who are able to understand the international needs of Real Madrid."
Perez added: "Now you [Courtois] have a great challenge, I am sure you can fulfil the wishes of all Madridistas. You know the city of Madrid is your home, your heart is here with your children and now the Santiago Bernabeu is part of your family as well.
"Thank you for taking on the challenge with the best and most prestigious club in the world."
Madrid face Atleti in the UEFA Super Cup in Tallinn next week before beginning their 2018-19 LaLiga campaign against Getafe.