Officers arrested the men after catching them trying to rob the expensive watch from a victim on Lisle Street in Soho at around 2.45am on Friday.
The officers – who had been deployed to the area specifically to combat watch robberies - arrested all three men on suspicion of robbery.
The victim was unharmed and the watch was returned to him.
Detective Scott Ware, of the AW Proactive Unit which covers central London, said: “We are acutely aware of the impact street robbery has on victims and that is why we have deployed officers in and around central London with the specific aim of stopping those determined to commit offences in their tracks.
“This an excellent example of the precise community crime-fighting model the Commissioner has put at the heart of his vision for the Met. This approach uses data and intelligence to deploy resources to where they are most needed.
“We will utilise all our resources, both local and our specialist teams, to ensure Londoners get the best response from their police service.”
The three men who were arrested have been charged with robbery.