Ipswich had an upset in their sights when the Championship side reached half-time at 0-0, but second half goals from Nicklas Bendtner, Laurent Koscielny and Cesc Fabregas sealed a 3-1 aggregate victory.
The Gunners will face West Ham or Birmingham at Wembley and Arsenal manager Arsene Wenger is now one win away from ending his six-year run without a trophy.
"We showed great spirit. It was a pleasure to watch the team," Wenger said.
"There was some great play and the team had an outstanding attitude. It was important not to concede and important to be patient.
"One or two years ago we would have been nervous but today we kept our focus on playing our game."
Looking to reach their first Wembley final since England's national stadium was reopened in 2007, Arsenal were expected to mount immediate pressure on Marton Fulop's goal to cancel out the 1-0 deficit from the first leg at Portman Road.
But Grant Leadbitter almost shocked Arsenal in the first seconds of the match - just clearing the crossbar with a shot from the halfway line as Ipswich kicked off - then the hosts started pouring forward with their attacks.
Fabregas had a drive saved by Fulop, Robin van Persie struck the crossbar with a header and Bendtner had an effort bravely blocked by Ipswich centre-back Damien Delaney.
One attack, however, sparked anger when Fabregas was challenged in the penalty area by Gareth McAuley, with replays suggesting the Spain midfielder went to ground easily.
Fabregas had used his programme notes to express his surprise at Wigan manager Roberto Martinez accusing him of gamesmanship during the Premier League clash at the weekend.
"He has said himself that he knows me well, in which case he should know that I am not the kind of guy that dives," wrote the Arsenal skipper.
Fabregas had the final clear chance of the first half when he was sent through by a delicate chip over the Ipswich defence by Jack Wilshere.
Only Fulop stood between Fabregas and the opener but the midfielder fired his left-footed volley wide of the Ipswich goalkeeper's post.
Arsenal had been forced into a first-half change when France defender Bacary Sagna collided with goalkeeper Wojciech Szczesny and needed treatment for a head injury.
And they grew increasingly frustrated in the first half, with Koscielny picking up a yellow card from referee Mark Halsey for a foul on Ipswich captain David Norris.
The second half started like the first, with Ipswich creating a chance as they looked to extend their aggregate lead.
This time Arsenal failed to clear a corner and defender Darren O'Dea flashed a volley across the face of goal.
Again, they had to repel plenty of Arsenal attacks, although the hosts were guilty of failing to shoot, and passing instead, when they were within sight of goal.
The breakthrough came in the 61st minute when Wilshere swept a ball to Bendtner, who cut inside Carlos Edwards and curled into the bottom corner.
Koscielny edged Arsenal ahead three minutes later when he headed home powerfully from an Andrey Arshavin corner.
Fabregas's goal came when Arshavin played him through and he finished neatly in the 77th minute.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional