Barca's tremendous threesome of Lionel Messi, Luis Suarez and Neymar did the damage as Luis Enrique's side ended the Gunners run at this stage of the competition for the sixth-straight season with a 5-1 aggregate result.
Holding a 2-0 lead following last month's first leg in London, the reigning European champions began quickly in a bid to leave Arsenal straggling behind.
Arsenal managed to get some footing back into the contest six minutes into the second half when Mohamed El Nenny opened up his Gunners account in fine fashion when he ran onto a nice ball from Alexis Sanchez and produced a lovely curling effort from the edge of the area.
Less than 15 minutes later, Barcelona snuffed out any risk of an Arsenal comeback when Dani Alves floated in a dangerous ball from the right which saw Suarez rattle home a spectacular volley, which appeared to rocket off his shin.
The contest was put to rest in the 88th minute when Argentine maestro Messi took possession of a loose ball in the area and walked his way in before deftly clipping over Ospina for his sixth Champions League goal of the campaign.
In the 80th minute, Barca goalkeeper Marc-Andre Ter Stegen came up with an outrageous one-handed double save to keep out Sanchez's free-kick before standing up strongly to deny Olivier Giroud's follow-up.
There were great chances throughout for both sides with Ospina managing to keep out Messi in the 17th minute after a lovely ball from Neymar, before the Colombian got down low to thwart Neymar on the half-hour mark.
In the 56th minute, Ospina again did well to deny Messi after Arsenal had awoken the Barcelona beast prior to Mascherano coming up with a goal-saving tackle on Danny Welbeck who perhaps could have taken an extra touch.
It was a spirited display from Arsene Wenger's side but the Catalan giants were at their best when they needed to be and move through comfortably to the quarter-finals where they join Spanish rivals Real Madrid and Atletico Madrid, Paris Saint-Germain, Manchester City, Wolfsburg, Benfica and Bayern Munich.
2015-16 UEFA Champions League - Round of 16 second leg