Mr Meenan’s body was found in an alleyway behind Creggan Street on Sunday, November 25, 2018.
Sean Rodgers, 34, of no fixed abode, and Ryan Walters, 22, from Station Park in Crossgar, denied murder.
A jury on Tuesday found Rodgers guilty of murder, and Walters not guilty of murder, but guilty of manslaughter.
A third man, Derek Creswell, 29, of King’s Lane in Ballykelly, had already pleaded guilty.
Walters was also found guilty of assault on William McConnell – a friend of Mr Meenan’s – on the same date.
After a trial lasting six weeks, the jury deliberated for 10 hours before returning a verdict.
During the Derry Crown Court trial, sitting in Belfast, the jury was told Mr Meenan sustained 52 stab wounds and there were more than 100 signs of assault, including two broken legs.
After the verdict, Judge Donna McColgan QC thanked the jury, describing them as “the most attentive I have ever come across”.
She told Rodgers the only sentence she could pass was a life sentence.
A tariff hearing will be held at a later date to determine the minimum time he will serve.
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