Judge Fernando Paredes will sentence him to between 15 and 20 years at a later date.
Members of the Dubliner's family, sitting in the public gallery, cried out "Oh my God!" in shock.
As he was led away to the cells in handcuffs, Burke told them: "Don't worry, I will be okay."
Burke's then girlfriend Sara Stuart, (30) was convicted of wounding the Spaniard's girlfriend Laura Negrin. She was cleared of the more serious charge of wounding Laura by hitting her around the head with a rock.
Stuart, who was in tears as the verdicts were read out, has spent nine months on remand. She is expected to receive a suspended sentence.
Outside court, the victim's mother Maria Teresa said: "Nothing will ever bring my wonderful son Abraham back. But we came here to see justice done on his behalf, and justice was done."
The tragedy happened as both couples were making their way home from separate nights in the resort of Playa de las Americas on April 30, 2010.
Burke and Stuart his girlfriend of nine months, also from Dublin, had arrived on the island three weeks earlier looking for casual work.
The Irishman had drunk wine, beer, whisky, vodka, and cocktails and had taken two tranquilliser tablets on the night of the killing, the court heard.
Stuart had downed a bottle of wine, ten vodkas, beers and shots, while the Spaniards had drunk at least ten whiskies each.
The fight broke out outside a hotel when the victim's girlfriend opened a car door, accidentally banging it into Stuart. Burke and Mr Baez exchanged blows.
Burke then went off to the couple's holiday apartment and returned moments later carrying a kitchen knife with a jagged 9cm blade. He stabbed Mr Baez in the face and shoulder before plunging the blade in the victim's neck.
The jury was read excerpts from daily love letters Burke had written from prison to Stuart in which he confessed to killing Mr Baez.