The group were allegedly posing as plain clothes officers who were approaching visitors and asking them to hand over cash or credit cards.
The three men, aged between 27 and 35, were arrested in Russell Square, central London yesterday afternoon.
Detective Superintendent Steve Osborn, Metropolitan Police Service, Westminster borough, said: "Millions of visitors to London will sadly always be an attraction to criminals and it is important that people stay alert.
"We have officers out there on the street identifying and arresting those who are involved in crime. I'm very pleased with the arrests my officers made yesterday, there have been number of incidents where criminals have impersonated police officers to take money off unsuspecting tourists.
"Officers would never take money from you, they would never take you to a cash point and ask you for money. They are unlikely to ask to see your bank cards and would never need to ask you for your pin number.
"Always ask to see an officers warrant card and inspect it, if in any doubt of the validity of an officer, call 999 and ask a uniformed officer to attend."
Olympic visitors have been warned to beware of gangs of criminals who use fake warrant cards to con them out of money.
Last month senior officers said some thieves were targeting tourists claiming they had to pay on the spot fines for trumped up offences.
Despite the fact many of the criminals could not speak fluent English, it is feared scores of tourists have already fallen victim to the scam.
Detective Superintendent Nick Downing, head of Operation Podium, said the "confusion" caused over neither the offender or victim speaking English very well, could be helping in the scam.
Some people have also been sucked in because they are from cultures which have a strong respect for people in authority, he added.
In addition Operation Podium officers have also charged 10 people with various offences relating to Olympic and Paralympic Games tickets since the 2012 Games opened on Friday.
Eight people have been charged with ticket touting, one person with theft and one person with handling stolen goods.
They will appear at various courts at dates in the future.
A further three people have been arrested today on suspicion of ticketing offences.
Two were arrested outside Horseguards Parade where the beach volleyball competition is taking place and a third at The Mile Walk, Lea Valley, where the canoeing is being held.