Jason Roy hit a blistering 85 as England reached a victory target of 224 with a mammoth 107 balls to spare after bowling out Australia for 223.
Openers Roy and Jonny Bairstow (34) put on 124 for the first wicket, their fourth consecutive century stand.
England, losing finalists in 1979, 1987 and 1992, will now face New Zealand, who have also yet to win the World Cup, in Sunday’s title match at Lord’s.
The Black Caps, runners-up to Australia in 2015, enjoyed a surprise semi-final win over India on Wednesday.
Four years after a woeful World Cup campaign triggered a major overhaul of England’s one-day international set-up, captain Eoin Morgan admitted reaching the final was a reward for his team’s hard work.
“If you told me after the last World Cup that we’d reach the final I wouldn’t have believed you. It sums up how far we have come in the last four years. Everyone should take a huge amount of credit,” Morgan said.
“Today was close to a perfect performance. Chris Woakes and Jofra Archer bowled a hell of a spell.”
“This final is a huge opportunity for us,” he added. “Making the most of it would be brilliant but getting to the final alone is awesome.”
Defeat meant Australia suffered their first loss in eight World Cup semi-finals and skipper Aaron Finch conceded they had been dominated from start to finish.
“We were totally outplayed today. We expected the new ball to seam a little but they bowled a great length, hitting the stumps a lot,” he said.
“We came here thinking we could win the tournament. We’ve had backs to the wall. I’m proud of how the group have progressed but it still hurts.”
Roy, who missed three matches earlier in the tournament with a torn hamstring, was in particularly good form, hitting five sixes.
Australia were in desperate need of early wickets after suffering a top-order collapse on the way to being dismissed for 223, with the record five-time champions thankful for Steve Smith’s battling 85.
All three of England’s defeats this tournament – including a group-stage loss to Australia – have come batting second but Roy and Bairstow showed few signs of nerves in Birmingham.
Smith, who bowled a single over that cost 21 runs, was booed by a large crowd, a reflection of the former Australia captain’s role in a ball-tampering scandal in South Africa that saw him banned for 12 months.
But the jeers turned to cheers as Roy hit three huge straight sixes in as many balls off his leg-spin.
Bairstow fell lbw to Mitchell Starc, who in the process set a new record for most wickets at a single World Cup of 27.
Roy was in sight of a hundred when he was given out caught behind down the legside by wicketkeeper Alex Carey off fast bowler Pat Cummins.
The batsman was visibly angry and had to be ushered away from the crease by square-leg umpire Marais Erasmus. England had earlier squandered their lone review.
But Joe Root (49 not out) and Morgan (45 not out) finished the job as the crowd chanted “Cricket’s coming home”.
Earlier, England paceman Woakes and spinner Adil Rashid each took three wickets.
Woakes, voted man of the match for his lethal spell of 3-20, struck twice early on as Australia slumped to 14-3 after winning the toss.
Australia’s prolific opening pair of David Warner and Finch, as well as Peter Handscomb, were all back in the pavilion by the seventh over.
Warner, who like Smith walked out to boos because of his role in the ball-tampering scandal, returned to even louder cat-calls after being dismissed for nine.
Smith and Alex Carey steadied the innings with a fourth-wicket stand of 103 but wickets tumbled at regular intervals and Australia were unable to halt England’s sprint to the final.