The Gunners - who were already leading 2-0 from the first leg in Holland - impressed from kick-off and it was no surprise when they went ahead through French midfielder Samir Nasri after 27 minutes.
Captain William Gallas added another at the start of the second half, before England hopeful Theo Walcott got the goal his all-action display merited and Nicklas Bendtner tapped in late on to make it a miserable return home for former national-team head coach McClaren, who must now make do with the UEFA Cup.
For Arsenal, though, an estimated £25million jackpot awaits following qualification to Europe's elite club competition for an 11th straight campaign.
• Display delights Wenger
It certainly was a controlled start by the hosts, who forced the first corner after five minutes following a brave run by Walcott down the right.
The delivery from Robin van Persie flew across the six-yard box, but no-one was able to get a touch.
Denilson gave the ball away carelessly on the edge of the Arsenal penalty, but was fortunate Theo Janssen drove his low shot wide.
Twente defender Cheick Tiote fouled Bendtner 20 yards out, conceding a free-kick in a dangerous, central position.
Van Persie struck it well, but his effort was too straight and Nicolay Mihaylov collected comfortably.
Arsenal continued to dominate and it seemed only a matter of time before their aggregate lead was extended to wrap up the tie.
Nasri did well to stay on his feet and nip in down the left before cutting the ball back into the path of van Persie - only for the Dutchman to blaze his effort high over the crossbar.
The goal eventually came after 27 minutes.
Walcott broke down the right once more, and pulled the ball back to the far side of the box where van Persie stretched to prod it into the path of Nasri.
The £12million Frenchman weaved past his marker before sending in a low shot, which took a slight defection as it rolled into the net.
It was no more than the hosts deserved, with McClaren's men having been pressed onto the back foot from kick-off as the Gunners marched towards the Champions League proper again.
Arsenal now looked back to their free-flowing best - and Denilson should have added a second when another slick passing move released the Brazilian into the right side of the Twente box, but his low shot was blocked by the legs of Mihaylov.
The Gunners contrived to miss a string of further golden opportunities before the break - van Persie somehow curling a sitter wide from 10 yards after Walcott had again broken down the right.
Nasri - who missed the first leg a fortnight ago because of injury - was given a rest at the restart, replaced by Emmanuel Eboue.
The hosts continued their aggressive approach and doubled their advantage after 52 minutes.
The ball dropped to Bendtner on the left side of the penalty area and he cut inside before firing in a low shot, which the Twente keeper could only push back into the path of captain Gallas - who slotted home from close range, just as he had done in the first leg.
With the contest now over, it just seemed a matter of how many Arsenal would score to further embarrass the former England boss, who had entered this tie hoping to prove a point or two.
To their credit, Twente - playing with three frontmen - continued to push forward, but that left them vulnerable on the break. Wenger made more changes as the match entered the final 25 minutes with Togo frontman Emmanuel Adebayor replacing van Persie.
It was 3-0 soon after when Walcott scampered clear and produced a cool finish into the bottom right corner to get the goal his performance merited.
With the job now done there was no point in taking any risks and so Cesc Fabregas - in his first appearance of the season after a hamstring injury - came off for Alex Song - the Cameroon man just back from the Olympics.
Bendtner added a tap-in with a minute left, but for McClaren, the final whistle could not come soon enough.
Display delights WengerArsene Wenger felt Arsenal had given him just what he asked for in the
comprehensive 6-0 aggregate demolition of Steve McClaren's FC Twente to secure a
place in the lucrative group stages of the Champions League.
'It was a big game for us and I felt we were well organised, disciplined and
focused. We were never really under threat,' said Wenger. 'It was important not to make mistakes. We were patient and scored our
goals.'
The Arsenal manager declared: 'The response was clear - togetherness, focus
and efficiency. We want to play with the best and to do that, we had to qualify for the group
stage. It was a big mental test.
'The whole team was sharper and physically much better tonight than on
Saturday and that is why it made it easier. They man-marked all over the pitch and did not take many risks.'
Cesc Fabregas was back in the starting XI tonight following a hamstring
problem.
Wenger said: 'He brings calm and confidence to the side and overall we had a
good balance today in the side. Cesc could have stayed on, he always wants to play, but he was probably more
disappointed that they did not have a go at us.'
Wenger hailed the performance of Walcott, who would have done his international
ambitions no harm at all with a sublime finish after a positive run.
'I have always said we have to be patient with him,' observed the Arsenal
manager. 'I felt he can be decisive in any game against anybody, if we can get him in.
'He has improved his first touch and his link-up play, which was vital for his
progression. For a while he has worked on a lot of things, and he has looked to have
improved and found that right balance between individual play and the team
play.
'But the way he finished tonight, you cannot teach that, he has that
naturally.'
Wenger hopes to add at least one new player to his squad before the transfer
window closes next week, most probably a midfielder.
However, the Arsenal manager accepted it is not proving a straightforward
process.
He said: 'You can see many transfers announced in the media every day - but it
takes a lot of time and does not always happen.'
For McClaren, it is now all about maintaining Twente's progress in the Dutch
league and building a European campaign in the UEFA Cup.
The former England manager said: 'I was sat here yesterday and they were
talking about a crisis at Arsenal. Someone said it was the best time to play
them after they lost to Fulham, but it was the worst time.
'We are hurt and disappointed. It's not how we expect Twente to play. We must
take that anger into Saturday's match when the season starts. Arsenal are further on than us. They have played Premier League games and it
showed. They were fitter and stronger than they were two weeks ago.
'We played with belief and competed with them in the first leg. We didn't do
that today. It's been a great experience for the players. They are a young team and they
need these experiences to learn.
'We are in the UEFA Cup, the season starts on Saturday and there is still a
lot to play for.'
McClaren added: 'Who knows if Arsenal can win it. It is a long hard
competition, but why not?'
Arsenal 4 - 0 Twente Enschede
