The relevant documentation was passed by the Italian authorities on Monday as the 20-year-old joined forces with Vladimir Petkovic's squad.
Perea joins the club on a five-year deal said to be worth in the region of 2.5million euros.
The Colombian Under 20 international started his career in the Deportivo Cali youth ranks before progressing to the senior squad, where he made 54 appearance.
During a two-year spell in the first team, Perea became a central part of the club's attacking force, scoring 10 goals before opting to take on a new challenge overseas.
Perea's arrival at the Stadio Olimpico blocks the potential signing of Turkish international Burak Yilmaz as the club have no more EU player spaces remaining.