Reza Baksh, 51, of Atlantic Avenue, Glencoe, was pronounced dead on arrival at the St Clair private hospital just before 5 pm.
According to reports, his wife Elizabeth had arrived home just after 4 pm yesterday when she was confronted by a gunman.
She was robbed and then taken into their house, where Reza laid relaxing in bed.
The gunman reportedly pulled his gun on Reza, took him outside, and shot him in his head.
At the scene yesterday, neighbours watched in horror as their quiet community turned into a crime scene, with no one being allowed to enter, or leave, the dead end road.
Insp Henry Dann and Sgt Andrew Lawrence coordinated investigations at the scene, and were searching for the suspect up to late yesterday.
PC De Gale also visited the scene.