Most of those arrested were from Manchester and Liverpool, it is said.
In a press release, the armed corps pointed out that as part of an operation codenamed Tatum, a criminal organization that distributed drugs in tourist areas was dismantled in the town of Magaluf.
Footage showed a man being led into court in handcuffs.
Twelve of the alleged drug dealers were taken to a court in the Majorcan capital Palma on Saturday and were remanded in custody following a private hearing.
Around £100,000 in cash was also seized by police during the dawn raids on Thursday.
Spain's interior minister Juan Ignacio Zoido used his official Twitter account to write: "Congratulations to the Civil Guard for dismantling a gang selling cocaine in Magaluf".
Several of the suspects frogmarched to court in handcuffs on Saturday were women. Most of the detainees were from Liverpool and Manchester
According to local reports, they were selling around eight kilograms of cocaine a month and were smuggling drugs into Majorca in speedboats.
In the operation, during which 12 homes were raided, authorities seized three kilograms of cocaine, smaller amounts of other drugs, 103,000 euros in cash and four vehicles.
Operation Tatum, which took place in the early hours of Thursday morning, resulted in the seizure of 3.5 kilos of cocaine - worth around £150,000.
Confirming 12 Brits were among the 14 arrested, the force added: "Officers from Britain's National Crime Agency have cooperated with the Civil Guard to detain the members of this organisation". "There are 14 detainees".
The operation was linked to a significant drug bust made in Majorca a year ago, which saw five Brits arrested as part of "Operation Daju".