One of the arrests took place at the island airport as the suspect was about to board a plane to the Spanish mainland.
The robbery happened last week in the Ibizan party resort of San Antonio.
A spokesman for the Civil Guard said: “The victim said two well-built men mugged him and pulled him to the ground before pulling the watch off his wrist.
“Detectives identified one of the men believed to have been involved and when they discovered his alleged accomplice was about to leave the island, alerted colleagues at the airport who were able to arrest him as he boarded a plane.”
Neither suspect has been named.
Rolex robbers, who are usually from the Italian city of Naples, target holidaymakers every summer in places like Ibiza and Majorca as well as Barcelona.