The explosion happened aboard Daallo Airlines Airbus A321 about 15 minutes after the jet, with 75 passengers, took off from Mogadishu airport.
Abdiweli Mohamed Maow, a former senior security officer at the Mogadishu airport, was convicted of preparing the laptop computer used to bomb the plane. Areys Hashi Abdi was convicted in absentia.
The attack, which was claimed by the Islamic extremist group al-Shabab, killed one passenger, Abdullahi Abdisalam Borle, who was thought to be the suspected suicide bomber. A body believed to be Borle's was found in a town north of Mogadishu.
Somalia faces an insurgency by al-Shabab, which has carried out deadly attacks in Somalia and neighboring countries.