Ben Purdy, 18, was shot in the head in Bermondsey after confronting his girlfriend's ex about "threatening" messages sent after their break-up.
Andrew Bayne, 37, of Trundleys Terrace, and his nephew Michael Bagnall, 22, of Hospital Way - both in Lewisham - were found guilty of the murder.
They will be sentenced at the Old Bailey on 20 November.
The court heard Mr Purdy and two of his friends - Callum Malone and Jack Walker - confronted Bagnell, and, following the "skirmish" last November, the defendants drove around Bermondsey looking for Mr Purdy.
When they found him in Mossington Gardens, Andrew Bayne shot Mr Purdy in the head then pointed the gun towards Callum before making off.
Mr Purdy suffered "catastrophic injuries" and died the next day, the court heard.
Despite the fact Bagnall had a new girlfriend, prosecutor Crispin Aylett QC told jurors, it still "rankled" that she had moved on and he sent her "threatening messages" by phone and on Facebook.
Mr Aylett said: "Ben obviously had enough and so that Sunday, around lunchtime, with two friends to help - Callum and Jack - the three of them decided to go and confront Michael Bagnall and have it out with him.
"It was undoubtedly a very stupid thing to have sought to do and cost Ben Purdy his life."
Bayne was also convicted of possessing a gun with intent and Bagnall of affray.
As the guilty verdicts were delivered, Michael Bagnall began shouting and swearing in the dock and had to be removed by officers.
Two family members have been convicted of shooting dead an 18-year-old in south London to "teach him a lesson".