The 19-year-old is the second arrival of the Andre Villas-Boas era and will link up with his new team-mates at the end of Spain's Under-20 World Cup campaign.
Barca confirmed Chelsea had paid 5million euros for the midfielder, with the deal including a buy-back clause of 10million euros after one year and 15million euros after two.
The fee was agreed 11 days ago for the midfielder, who was quoted this week as saying: "Chelsea is a great option for me.
"Leaving Barca hurts, but you have to take your chances."
Oriol's agent, Magico Diaz, reportedly jetted out to Columbia this week to seal the deal.