The Serie A high-flyers have stumped up an initial €2.5 million to take the Colombia international until the end of the campaign and will have to pay another €12.5m to make the move full time.
It marks Roma's second foray into the transfer market in as many days after they striker Seydou Doumbia joined from CSKA Moscow on Saturday.
Ibarbo moved to Cagliari ahead of the 2011-12 season and has gone on to make 115 league appearances, scoring 15 goals.
Head coach Rudi Garcia has moved quick to bolster his forward options after Mattia Destro departed for Serie A rivals Milan on Friday.
Cagliari have also wasted little time in sourcing a replacement for Ibarbo with Paul-Jose M'Poku arriving on loan from Standard Liege.
The 22-year-old left Liege in 2008 for Premier League club Tottenham, but failed to break into the first-team picture at White Hart Lane and returned to the Belgian club in July 2011.
