Monchi spent 17 years in the same role at Sevilla, with nine of the 13 trophies in the club's 127-history coming during that time, including three successive Europa League wins. Sevilla also won its predecessor the UEFA Cup twice.
The former goalkeeper was renowned for bringing in talented players on a slender budget, attracting the likes of Dani Alves, Ivan Rakitic, Julio Baptista, Grzegorz Krychowiak and Kevin Gameiro and selling them on for bigger fees.
Monchi's record made him a target for a host of European clubs since he left Sevilla in March.
"I couldn't be happier with this appointment, as Monchi is widely regarded as one of the best minds in world football," said Roma president James Pallotta.
Monchi spent his entire playing career with Sevilla, emerging through the club's youth system before going to be become a member of the first team squad from 1990-1999. He became sporting director a year after retiring.
"This is an exciting project and I look forward to serving the supporters, staff and players at this iconic club for many years to come," said Monchi.
AS Roma became the first Serie A club to be foreign owned in 2011 after an American group fronted by Boston businessman Thomas DiBenedetto completed a takeover.
Roma have yet to win a major trophy under the new owners although they have twice finished runners-up to Juventus in Serie A in the past four years.
(Writing by Brian Homewood)