Kiaran Stapleton walked up to stranger Anuj Bidve, 23, in the street in Salford, Greater Manchester, and shot him in the head at point blank range.
Stapleton, 21, had admitted manslaughter on the grounds of diminished responsibility but a jury at Manchester Crown Court rejected that defence and convicted him of murder. He will be sentenced today.
Nazir Afzal, chief crown prosecutor for the North West said Mr Bidve's senseless murder had "shocked and appalled us all".
He added: "Kiaran Stapleton shot Anuj, an innocent and defenceless man, at close range without warning or provocation.
"Thankfully such crimes of truly random and brutal violence are extremely rare.
"It was a cowardly murder, and his reaction afterwards in trying to cover his tracks, hide from police and evade justice was also cowardly. Since the moment he killed Anuj he has shown no trace of remorse and no concern for the pain Anuj's family are going through."
Mr Afzal told the court that two days after the murder Stapleton went to a tattoo parlour and had a teardrop design placed below his right eye – a symbol used by some gangs to show the wearer has killed someone.
The prosecutor said: "It was a sign, we say, that he was boasting about the murder, that he thought it gave him some sort of notoriety.
"Only when he realised the evidence against him was overwhelming did he plead guilty to manslaughter, admitting he pulled the trigger but claiming that at the time of the killing his responsibility for his actions was diminished."
Mr Bidve had arrived in the UK last September to embark on postgraduate studies in micro-electronics. He was visiting Salford with a group of friends from Lancaster University last Christmas.
They left their hotel in the early hours of Boxing Day to queue early for the sales when their paths crossed with Stapleton's.
Stapleton calmly walked across the road and repeatedly asked for the time. When someone finally answered he pulled a handgun out of his pocket and fired one shot to Mr Bidve's left temple.
He was then seen to smirk or laugh over his victim's body before he ran off to his nearby home in Ordsall. The weapon, which fired a 9mm bullet, has never been found.
Mr Bidve never regained consciousness and was pronounced dead in hospital.
Stapleton later told a psychologist in prison that he picked out his victim because "he had the biggest head".
Both the prosecution and defence agreed Stapleton had a recognised medical condition, an anti-social personality disorder.
He showed traits of callousness, impulsiveness, anger, lack of remorse and incapacity to experience guilt.
The defence claimed he suffered from an abnormality of mental functioning because of the disorder and said it probably substantially impaired his ability to exercise self-control.
That was the most likely cause or a significant contributory factor as to why he shot Mr Bidve, they argued during five weeks of evidence. However, the jury rejected that argument less than two hours and 15 minutes after retiring to consider its verdict.
Mr Bidve's parents, Subhash and Yogini, flew from their home in Pune, India, to attend the trial and each day listened intently to the evidence from the front row of the public gallery.
As the verdict was delivered. Mrs Bidve cried and Mr Bidve bowed in his seat and later held his hands to his face.
Mr Afzal added: "Anuj had his whole life ahead of him. He was young and bright, a talented student who was enjoying his time at Lancaster University.
"His parents were understandably very proud of him. They sent him to the UK to continue his studies and fulfil his ambitions but tragically came here themselves to take his body back home.
"My thoughts and sympathies are very much with them."