The 48-year-old was murdered outside his home on Chester Street at around 8pm on Wednesday evening.
Welsh was shot in the back of the head after arriving back from training at Holyrood Boxing Gym, which he owned, and was pronounced dead at the scene.
Tributes have been paid to the lifelong Hibs fan since his death, with one supporter believing the Easter Road support should pay their respects during the upcoming Ladbrokes Premiership match.
Connaire Wallace wrote on Twitter: “Think it would be no less than Brad deserves to have a 48th minute applause this Sunday in our match against Celtic with “One Bradley Welsh” ringing around the stands.”
The tweet has close to 300 likes at the time of writing.
Detectives are refusing to rule out an organised crime group being responsible for the fatal attack and insist they will delve into his past as part of the extensive investigation in an effort to discover why the charity worker was targeted.
Detective superintendent Allan Burton said: “We have nothing to indicate that it is connected to anything else but we’ve got to bear that in mind and look into the background of Mr Welsh’s lifestyle, association and other crimes that have taken place.
“Mr Welsh’s family are devastated and have no intention of seeking retaliation."
Meanwhile, murals of Welsh have popped up around the Easter Road area, including one on the Crawford Bridge, known to supporters as ‘The Bridge of Doom’.
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