The one-sided victory ensured a 14th trophy to end Guardiola's incredible four-year reign as the outgoing coach hands the reins to his assistant Tito Vilanova.
Lionel Messi had already come within inches of giving Barca the lead before they went ahead in the third minute as Pedro turned home a loose ball after Xavi's corner had deflected into his path.
Gorka Iraizoz made a fantastic save to deny Messi his 73rd goal of the season moments later, but the Argentinian was not to be denied and fired home from a narrow angle before Pedro doubled his tally with a fine finish midway through the half.
Athletic were perhaps unfortunate not to be awarded a penalty that could have changed the face of the game before half-time as Fernando Llorente was pulled back by Gerard Pique, and Barca comfortably saw the game out after the break.
Messi broke free inside the first 30 seconds and fired a warning shot inches past Iraizoz's right-hand post before Pedro also had a goalbound effort defected just wide.
However, from the resulting corner Pique's header rebounded off Javi Martinez and fell perfectly for Pedro to sweep home his 12th goal of the season.
Barca were completely dominant in the opening quarter and Messi nearly had a spectacular second when his curling effort from just outside the area was clawed away at full stretch by Iraizoz while Xavi also fired just over from range.
The killer second goal was coming, though, and it arrived after 20 minutes thanks to a brilliant defence-splitting pass from Andres Iniesta which put Messi in the clear, and even on his weaker right foot the brilliant forward gave Iraizoz no chance.
Four minutes later it was three as Pique played a quick free-kick into Messi and his pass was stroked home clinically from 20 yards by Pedro.
Athletic had to wait 26 minutes for their first attempt on goal as Jose Manuel Pinto parried Markel Susaeta's fierce drive to safety but moments later the Basque side had a major reason for complaint as Llorente appeared to be felled by Pique when clean through on goal.
The defender certainly appeared to have a hold of his Spain colleague's shirt and would most likely have been sent off for denying a clear goalscoring opportunity had the penalty been awarded.
Ibai Gomez had Athletic's best chance of the game six minutes into the second half as Ander Herrera played him in behind Adriano but his chip over Pinto floated just wide.
Messi then nearly capped another classic performance with 20 minutes remaining as he dashed past five Athletic defenders before Iraizoz blocked his low effort and no Barca player was following up to take advantage of the rebound.
Athletic had one final chance to get a consolation goal but Jon Aurtenetxe's wayward header when completely unmarked at the back post summed up their evening as Barca comfortably saw out the final moments to claim their 26th Copa del Rey title.
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