The 21-year-old Spaniard suffered the injury in the first-half of Saturday's 3-1 win at Sunderland and he went under the knife after he was assessed in London instead of flying to Japan for the Club World Cup.
Romeu joined from Barcelona last August and has forced his way into first-team contention in recent weeks, making nine appearances for the Blues this season.
A statement on Chelsea's website read: "Oriol Romeu underwent anterior cruciate reconstruction surgery and medial meniscus repair yesterday (Monday). He is expected to be out for six months."
The club have also confirmed that 19-year-old George Saville has been added to the squad for the Club World Cup as a replacement.
Chelsea take on CONCACAF Champions League winners Monterrey in the semi-final of the competition on Thursday.