Their flight from Slovenia to the UK was diverted to Cologne after the pilot was alerted to a "suspicious conversation" with "terrorist content".
"The criminal investigation against them has been halted. No evidence was found," police said.
"We now believe that there was never any real danger."
All 151 passengers were evacuated from the Airbus 319 aircraft using emergency slides, and nine received medical treatment.
The men, aged 31, 38 and 48, were returning to Stansted, in Essex, from Ljubljana on 10 June when the disruption arose. They are said to have been on a business trip.
According to prosecutors, the flight was diverted when fellow passengers reported the men were discussing "terrorist matters" and carrying a book entitled "Kill" with a sniper rifle on the cover.
They said the contents of the alleged conversation could not be verified.
No explosives were found in the passengers' luggage or on the plane. A backpack belonging to the men was nonetheless blown up by police.
The German tabloid newspaper Bild said passengers told airline staff they had heard the men using the words "bomb" and "explosive", and said one was carrying a suspicious rucksack.
A spokesman for Cologne-Bonn airport said: "The pilot had been informed about a suspicious conversation on board, after which he decided to make an unscheduled landing in Cologne-Bonn.
"After the safe landing... the 151 passengers left the [aircraft] via emergency slides and were taken to a transit gate."
The diverted plane landed in Stansted airport on Sunday.
Passenger Daniel Noonan told the BBC that armed police entered the aircraft and escorted two men off. The third was led away on the tarmac after the passengers had exited via the slides.
Passenger Richard Peters said he saw the two Asian men being handcuffed on the tarmac at Cologne-Bonn airport.
He added that people on the flight were quarantined for about nine hours while police interviewed passengers about the men.
He said: "To be fair spirits were quite high considering what had happened.
"In the current climate you have to take everything seriously. My suspicion is it was, hopefully, nothing sinister. But you have to take everything seriously.
"The right thing was done."
Another passenger, Dave Hargreaves, said: "In the flight I didn't see the suspects at all. But I noticed quite a bit of activity, with aircrew popping into the cockpit repeatedly. And a slower than normal serving of the food and drink service.
"Then at our cruising altitude I was surprised to see the air brakes go up on the wings and us start a rather speedy descent. It wasn't until perhaps 10 minutes later that we were told 'due to operational reasons' we would be diverting to Cologne airport."
Easyjet said the captain had taken the decision to land as a precaution to allow additional security checks to take place.
All the other passengers were given a hotel for the night, a spokeswoman said, adding: "We thank passengers for their understanding. The safety of Easyjet's passengers and crew is our highest priority."
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Three British men who were detained in Germany after their conversations on board an Easyjet flight sparked alarm have been released without charge.