Bukayo Saka's first-half finish — his second goal of the tie — was enough to seal a 2-1 aggregate victory at the Emirates Stadium, sending Arsenal to Budapest for the showpiece on 30 May where they will face either Bayern Munich or Paris Saint-Germain.
The win extends Arsenal's unbeaten run in the competition to 14 games — 11 wins and three draws — across a campaign in which they have conceded sparingly and dismantled every opponent placed in front of them.
Arteta was overcome at full-time, pointing immediately to the role the supporters played in setting the tone.
"It's one of the best nights that I've had in my career. I think today the supporters raised the standard and told us the way we had to play this game. The way they received the team outside the stadium was unique — I've never seen it before. And the energy that was created today in this stadium was something else. Something different. Something that elevates everybody's conviction, energy and passion — and I'm so proud."
The scenes contrasted sharply with this time last year, when Arsenal were eliminated at the semi-final stage by Paris Saint-Germain. On this occasion, despite occasional late pressure from Atletico Madrid, the Gunners managed the game intelligently in the closing stages, with substitute goalkeeper Kepa Arrizabalaga and both centre-backs David Raya and Gabriel making crucial interventions.
Arteta was emotional when reflecting on what the result means to everyone associated with the club.
"It's been so many years. It's only the second time in our history that we've achieved the final. There are days that I don't know what I'm doing with this job because it's just mad. But when I was looking at the stands today, at my players and the staff, and saw their joy and happiness and that light in them — everything we do makes sense."
He was fulsome in his praise for the performance itself.
"The team was immense. We played a really, really tough opponent who have so much experience playing in this kind of competition. The timing of the goal was perfect, I would say. We had that moment as well where it could have gone their way, and in the last few minutes I think we had to manage the game — and we did that really well."
Viktor Gyokeres, deployed as a second-half substitute, struck the crossbar with a close-range volley that would have secured the result in more emphatic fashion. Arteta credited the entire club — owners, board, staff and players — for seeing the journey through.
"Josh (Kroenke), all the board, all the staff — and that shows you how much it means to everybody and how important everybody is in this journey. I'm very grateful."
Arsenal face West Ham United at the London Stadium on Sunday as they continue their push for the Premier League title alongside the European final.
"Let's enjoy tonight, and tomorrow we have to start to recover really well, get the batteries to the maximum again, and start to prepare for West Ham — because that's a massive game."