Armed officers were sent to Chester Street in the city's west end at about 20:00 on Wednesday.
"Anyone who believes they have any relevant information should contact police immediately".
He gained notoriety by playing the role of Doyle in the 2017 British hit-flick "Trainspotting 2", which netted about $18 million in box office sales, according to IMDB.
In 1993, he was the lightweight champion in the Amateur Boxing Association (ABA) of England at only 17 years old, the youngest age allowed to register in the ABA. Officers will continue to provide a high-visibility presence in the area to engage with the public, offer reassurance and gather information that can assist with this investigation. "Then they said they've got a scene for me and Danny asked, 'Will you try out for a part?"
Irvine Welsh said his heart was broken over the news. Goodbye my incredible and handsome friend.
He previously appeared on the documentary series Danny Dyer's Deadliest Men in 2008.
Fraser Walker, chief operating officer of Boxing Scotland, said: "The Boxing Scotland family is extremely shocked and saddened by the sudden and tragic passing of Bradley. Our thoughts and sympathy go out to Bradley's family at this extremely hard time".
Tributes were paid on social media, with one woman posting a picture of her and friends alongside Welsh in a boxing ring.
Mr Morton, 46, said: "I came out the house and we were told to go back in. Our coach, our motivator but most importantly our friend, Brad Welsh".
The documentary series profiled some of the most unsafe men in the United Kingdom, and Welsh was featured on the sixth episode of the second season.
"We've not been told anything but police waved through some ambulances".