The 25-year-old Argentinian has passed a medical and agreed a four-year contract with the Spanish champions, and will be officially unveiled at the Bernabeu at 1pm local time on Friday.
"Negotiations with the club started a long time ago. I've always wanted to come here. It's easy to reach an agreement when both parties are interested."
"I want my first contact to be with the club's board members, followed by the coaching staff and my new team-mates.
"I would like to stay here a long time and to play as much as possible in order to prove what I can do. You earn good results by working well."
Saviola follows in the footsteps of new coach Bernd Schuster - as well as Michael Laudrup and Luis Figo - in making the switch from the Nou Camp to the Bernabeu.
He is not expecting a smooth path but is looking forward to getting down to business.
"I am psychologically prepared to start this new stage in my career," he said. "I must forget about the past and start a new at this great club. This is a very demanding institution.
"I knew some people wouldn't want me here at first as soon as I started negotiating with the club. I've always wanted to join an important institution such as this one."
Saviola insists he bears no ill-feeling towards Joan Laporta following the Barca president's suggestions the Catalans did not get their money's worth out of the South American on the pitch.
"I wish Barcelona's president had made those comments about me to my face as opposed to the press, but these things happen all the time," said Saviola, who becomes Madrid's third signing of the week following the acquisitions of defenders Pepe and Christoph Metzelder.