After accepting the plea of the MQM leader, the court directed Khan to submit two surety bonds of Rs1 million each.
Amir Khan will leave the country on September 18 and return on October 3.
After hearing arguments from both the sides, the ATC had reserved its verdict on August 15. The defence counsel of the MQM leader had contended in the court that name of his client was not in the Exit Control List.
Rangers, on the other hand, have expressed reservation over the decision and termed the documents insufficient to grant permission to the accused to leave the country.
In June, the ATC judge approved the bail plea of Amir Khan and ordered him to submit one million rupees bail amount.
The judge also observed that the accused being granted bail as the investigators failed to probe the case properly.
The court had also ordered the MQM leader not to leave the country.
MQM leader Khalid Maqbool Siddiqui and other party leaders were present during the hearing of the case.
It may be noted here that Siddiqui has left for Singapore for medical treatment.
Amir Khan, a member of the Muttahida Qaumi Movement Rabita Committee, was arrested along with others during a Rangers raid on the Nine-Zero, the party headquarters of MQM in Karachi, on March 11 this year.
The Rangers personnel brought 27 arrested men including Amir Khan and former MPA Yousuf Munir to the ATC amid stringent security measures at the court premises.
The hands of the accused were tied and they were blindfolded when they were brought to produce in the court.