Arbeloa put the finishing touches on his move after Madrid agreed a reported £3.5million deal with the English club for the versatile defender.
He is Real's seventh signing since Florentino Perez returned to the presidency in June, following in the footsteps of Cristiano Ronaldo, Kaka, Karim Benzema, Raul Albiol, Alvaro Negredo and Esteban Granero.
"Since the door was opened to the possibility of coming here I was hoping for it to happen with all my heart, and I'm very happy to be able to return," he told RealmadridTV.
"Not even in your best dreams can you imagine that you are going to be in the Real Madrid first team.
"Moreover, when you leave the club with the feeling of not being able to be in the first team, you know that it's very difficult to return, so for me, when this opportunity presented itself, my first objective was to take it and fortunately I'm here.
"I'm delighted and eager to take this opportunity and get out onto the pitch to train, to play and to enjoy it.
"I think that any kid, regardless of their team, would take advantage of the chance to come to Real Madrid, and especially with the sporting project here now."
Arbeloa is keen to help Madrid get back on the trophy trail next season, saying: "My objective is to give it everything in training and try to win myself a place in the team, which is the objective of any player. And of course I want to help my team-mates and the team to win titles, which in the end is what counts."