The attack, which took place in the underpass at Hockley Circus, Birmingham, has been described as "unprovoked and callous".
The 13-year-old boy and his friends had been in the city and were on their way to get food when he was attacked just before 7pm on November 18.
Despite his injuries, the boy managed to call 999 to tell the ambulance service he’d been injured.
Firearms officers were first on the scene and gave life-saving first aid before paramedics arrived.
Zidann Edwards and Diago Anderson, both 20, alongside a 17-year-old who cannot be named, were all convicted of attempted murder following a six-week trial at Birmingham Crown Court.
The 17-year-old was also charged with possession of a firearm with intent to endanger life and possession of a prohibited weapon.
All were found guilty of these crimes on August 2 and will be sentenced on October 7.
Police found CCTV evidence which showed a car travelling along the A41 before stopping abruptly on a service road. Edwards, Anderson and the 17-year-old got out.
The 13-year-old boy and his friends were then chased into the underpass and within seconds a homemade shotgun, known as a 'slam gun', was fired, shooting him in the back and leaving him paralysed.
The footage showed Edwards, of Ford Street, Hockley, Anderson, of no fixed address, and the 17-year-old boy running from the scene and driving off.
The trio were later tracked down, with the car they were in linked to them by forensic experts.
Following the arrests, police recovered more evidence including the clothing they wore on the day of the shooting, along with several phones.
Officers also found a handgun and a slam gun at an address linked to the 17-year-old and further examination helped to prove this was the weapon used in the shooting.
Detective Inspector Michelle Cordell, from force CID, said: "The unprovoked and callous actions of Zidann Edwards, Diago Anderson and the 17-year-old boy, changed the life of an innocent 13-year-old boy and his family forever.
"The impact of their actions are truly heartbreaking and my thoughts remain with the boy, his family and friends.
"From the outset, my team worked tirelessly with internal and external colleagues and partners to gather and present the evidence in this case. Their collective hard work and dedication led has helped achieve justice for the victim and his family.
"Our primary focus is always to prevent these incidents from happening, but sadly we do continue to see gun violence on our streets.
"We need our communities to come together to help us in our fight against gun and gang-related crime."