Mikel Arteta’s side settled the semi-final second leg with Saka’s strike late in the first half at an ecstatic Emirates Stadium.
The Gunners, who drew 1-1 in the first leg in Madrid last week, held firm after Saka’s goal to go through 2-1 on aggregate.
Arsenal will face Paris Saint-Germain or Bayern Munich in the final in Budapest on May 30.
Holders PSG, who beat Arsenal in the semi-finals last year, have a 5-4 lead ahead of the second leg in Munich on Wednesday.
It was a cathartic night for Arsenal, who are back in the Champions League final for the first time since losing 2-1 to Barcelona in their only previous appearance in the showpiece in 2006.
Arsenal have never won the Champions League, with their two major European trophies coming in the 1994 Cup Winners’ Cup and the 1970 Inter-Cities Fairs Cup.
Their last continental final ended in a 4-1 defeat against Chelsea in the 2019 Europa League.
It is shaping up to be Arsenal’s greatest ever season as they chase a Premier League and Champions League double.
Even Arsene Wenger’s ‘Invincibles’ – who won the club’s last English title in an unbeaten top-flight campaign in 2004 – might have to bow to the current generation if they finish the job.
Fittingly, it was Saka – the homegrown symbol of the Arteta era – who proved Arsenal’s match-winner.
Now just four games from immortality, Premier League leaders Arsenal were given a huge boost in the title race when second-placed Manchester City drew at Everton on Monday.
The Gunners will be crowned champions if they win their last three games against West Ham, Burnley and Crystal Palace.
Once the title is decided, Arsenal will head to Hungary with a maiden Champions League crown in their sights.
Arsenal endured jibes about their perceived lack of mental strength after a run of four defeats in six games in all competitions sparked painful memories of previous failures to end their six-year wait for silverware.
But the ‘nearly-men’ and ‘serial choker’ labels applied only weeks ago are on the verge of being banished forever. (AFP)