Madrid – looking for a new head coach following Zinedine Zidane's departure – confirmed the arrival of Alaba on a free transfer upon the expiry of his Bayern contract, the Austria star signing a five-year deal at the LaLiga giants.
Following Friday's confirmation, Alaba took to social media to talk up his move from Munich to the Spanish capital after winning 27 trophies with Bayern.
"I leave one special club for another," the 28-year-old Austria international Alaba wrote via Twitter.
"After so many years in Munich, I'll take on this new challenge and do my best to continue the history of this special club.
"I can't wait to play my first game in this legendary white shirt, in front of all of you, the Real Madrid fans.
"I'm convinced that this experience will be full of success."
Alaba made his debut in a DFB-Pokal meeting with Greuther Furth in February 2010, becoming the club's youngest player in history at the time and setting up a goal for Franck Ribery within a minute of coming on.
The Austrian was 17 years, seven months and 18 days old when he made his debut, but Jamal Musiala is now Bayern's youngest debutant.
Alaba has gone on to make 448 appearances for the Bavarian giants, scoring 35 goals and supplying 47 assists in all competitions.
He has won 27 trophies with Bayern, lifting the Bundesliga title 10 times and winning the Champions League twice – both of those European successes forming part of trebles.