The Bayern Munich winger signed for Roma on deadline day Monday in a whirlwind deal.
Zaragoza joins on-loan for the remainder of the season after spending the first-half of the campaign with Celta Vigo.
He told the Roma website: "It all happened suddenly. From one day to the next, they informed me that this possibility was available, and I didn't think twice; I said I wanted to come to Roma.
"I also want to thank the club, the owners, (director Ricky) Massara, (coach Gian Piero) Gasperini, and everyone else for giving me this opportunity."
Zaragoza also said: "I'm coming with high expectations, with great expectations. I want to be important for this club, win titles, and I hope we'll be playing in the Champions League next year."
On Roma coach Gian Piero Gasperini, the Spain international added: "I know him because last year I really liked the way his team played; they were great to watch and played really good football. I'm eager to begin this adventure and see what the coach can teach me.
"He'll help me, and I'll learn a lot from him."