Monchi spent his entire playing career at Sevilla before taking over as the club's sporting director in 2000, but the 48-year-old left his post in April.
Sevilla enjoyed a period of great success during Monchi's tenure, including five Europa League titles and two Copa del Rey triumphs, and although Monchi was strongly linked to several high-profile clubs across the continent, he decided on a move to the Italian capital.
"I believe Roma have already built a lot," Monchi told Roma's official website. "All we have to do is add to that and I believe that with good planning, the right personnel and infrastructure, we can achieve great things.
"The goal is to try to consolidate Roma not only at the top of Italian football, but also in the elite of European football.
"I believe this club is perfectly suited to the way I work. It's an ambitious club that wants to grow and compete for major honours.
"This is a wonderful city and the club have a huge fanbase. I believe we have everything we need to do a good job."
An American group fronted by Boston businessman Thomas DiBenedetto completed a takeover of Roma in 2011, though they have yet to win a major trophy under the current owners.
But Monchi has emphasised the need for patience, stating that it will take time to replicate the model he had in place at Sevilla.
"Planning is very important in the workplace. At Sevilla, we all contributed to building a model which grew over time and secured unimaginable results," Monchi, who has signed a four-year deal at Roma, added.
"The short-term goal is for me to get settled here and learn about the club's identity and philosophy.
"Then, [incumbent sporting director] Ricky Massara and I have to create the most professional football department possible because that's what I believe is one of the secrets to future success.
"If the fans are pleased with the job I do in the future, that would be the best recognition I could receive."