Mr Welsh, 48, was shot and killed on Chester Street in the West End of Edinburgh on Wednesday evening.
And Dyer took to his official Instagram account to post a photo of the pair together along with an emotional message.
The pair are thought to have crossed paths when Mr Welsh appeared on his hit TV show Danny Dyer's Deadliest Men in 2009.
Mr Bradley went on to play Mr Doyle in Trainspotting sequel Trainspotting 2.
READ MORE: Bradley Welsh: A tribute in pictures to Edinburgh boxer and Trainspotting 2 star
Dyer wrote on his official Instagram page: "So sad to hear the news about Bradley Welsh. A good soul with a massive heart. A massive loss. Rest in Peace my old son."
Detective Superintendent Allan Burton from the Major Investigation Team said: "At this time our deepest sympathies are with this man's family and a significant inquiry is now underway to trace everyone who was involved in the murder.
"I would ask that anyone who was within Chester Street, or the West End of Edinburgh on Wednesday evening, and who saw anyone, or anything suspicious, to contact the police immediately.
"Part of this investigation will focus on obtaining CCTV from nearby homes and businesses and we would also urge any motorists who were in the area and may have relevant dash-cam footage to share this with us.
"Murders remain extremely rare in the Capital, and such incidents where a firearm are used are even more uncommon. However, we wish to reassure the public that considerable resources are being dedicated to this inquiry and we are treating this matter with the utmost seriousness."