The three men were arrested and being questioned "on the suspicion of the preparation of a serious state-threatening violence," police said.
One backpack belonging to the men was blown up by police.
The arrests came after the Easyjet flight, from Ljubljana to Stansted airport in Essex, was diverted to Cologne-Bonn airport yesterday afternoon.
All the 151 passengers were evacuated and flights were suspended for three hours.
A spokesperson for Cologne-Bonn airport confirmed the landing and said: "Prior to this, the pilot had been informed about a suspicious conversation on board after which he decided to make an unscheduled landing in Cologne-Bonn".
The passengers had to "undergo a check immediately" and additional security checks were carried out on the plane.
A statement from Cologne police said other passengers had made the crew aware of the suspicious conversation by three men.
"During the flight, other passengers had made the crew aware of the men. According to the witnesses, these had been the subject of terrorist content. There upon the flight captain decided to carry out an evacuation in Cologne around 6 PM (local time)," the statement said.
Easyjet said the captain had taken the decision to land as a precaution to allow additional security checks to take place.
All the passengers had been given a hotel for the night and were flown back this morning.
"We thank passengers for their understanding. The safety of Easyjet's passengers and crew is our highest priority," the spokesperson added.
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