The tie was in the balance after a 1-1 draw in the first leg, but the Gunners were the dominant team from the start with Theo Walcott running Joan Capdevila ragged with his trickery and pace.
The 20-year-old wideman was able to go past the Spanish left-back with ease and whip balls into the penalty area.
After 10 minutes Arsenal took the lead with Cesc Fabregas flicking Emmanuel Eboue's pass into the path of Walcott, who chipped the ball exquisitely over advancing goalkeeper Diego Lopez.
After 28 minutes it was nearly 2-0 when a free-kick from Fabregas was tipped away by Lopez and Emmanuel Adebayor's follow up was cleared off the line.
Despite all their dominance in the first half, the Gunners had to be wary of only been 1-0 ahead and early on in the second period the Spanish club started to put them under pressure.
However, after 60 minutes Adebayor made it 2-0 after slotting the ball past Lopez in Villarreal's goal after receiving a perfect pass from Robin van Persie.
Eight minutes later it was game over for the Spaniards. Walcott was brought down in the penalty box by Diego Godin and protests from the Villarreal players led to Sebastian Eguren picking up his second booking to leave the visitors down to 10 men.
Van Persie coolly slotted the penalty into the right-hand corner of the net to make it 3-0 and game over.
Arsene Wenger's side can now look forward to a semi-final against fierce rivals Manchester United as the Gunners aim to continue their path to winning the Champions League for the very first time.