Officers boarded the aircraft after alarmed staff radioed ahead to ask for assistance dealing with the louts.
Anxious staff on the flight to Heraklion repeatedly warned the the three men about bad language and aggressive behaviour, but the drunks threatened to “do in” staff and other passengers .
They were drinking from a bottle of gin they had bought from duty free in breach of the airline’s rules.
When the flight touched down on Thursday evening the men, who are thought to be in their twenties, were whisked from their seats by waiting Greek officials.
The pilot apologised to passengers on the tannoy and said the company operated a zero tolerance policy over unruly passengers.
The holiday flight was full with families heading for Crete, and had left Edinburgh Airport that afternoon.
One shocked mum, who was on board with her three children, said: “It was obvious from the start the lads were drunk and there was going to be trouble.
“They were right at the back and kept pestering staff for drinks even before the plane had taken off from Edinburgh.
“But once it was in the air their language was a disgrace.
“It was the worst words imaginable and the hostesses constantly warned them to tone it down.
“Near the end of the flight one of the staff had a real go at them and said that was their final warning
“But once the plane landed the doors opened and the police came on to escort them off the flight.”
Phil Ward, managing director at Jet2.com, said: “We can confirm that our captain and crew called Greek Police to meet the aircraft so that three disruptive passengers could be offloaded, after they continued to ignore crew instructions and behave in an appalling and aggressive fashion on our Edinburgh to Heraklion flight.
“These disruptive passengers displayed unacceptable and aggressive behaviour to our crew and other customers, and the illicit consumption of alcohol on the aircraft was a major contributing factor.
“It’s something we see time and time again when incidents of disruptive passenger behaviour occur.
“This demonstrates yet again, why as part of our Onboard Together campaign, Jet2.com is continuing to call for action to better control the sale and consumption of alcohol and tax free goods at airports.
As a family friendly airline flying millions of people on holiday every year, we are demanding that proper action is taken to protect our crew and customers from this appalling behaviour.
“Fellow customers and families travelling for a well-earned holiday should not be subjected to this behaviour and we will be taking further action in support of our crew to ensure that those responsible are held accountable for their actions.”
The company has handed out lifetime bans, stopped people from travelling and threatened to pursue legal action against passengers whose behaviour results in a diversion.
Last month, Glasgow Airport chiefs and Police Scotland launched Campus Watch, a scheme designed to cut flight delays or cancellations caused by disruptive behaviour. Under the initiative, passengers are prevented from drinking alcohol bought in duty free shops in the airport or on flights and police will be informed when large group flight bookings - such as for hen and stag parties - have been made in an attempt to nip any potential trouble in the bud.