For just the second time in the past seven World Cups, Australia have failed to make the final, but Finch said he was proud of his team's efforts 12 months after they were crushed 5-0 by England in a one-day worldwide series.
Joe Root (49 not out) and Morgan (45 not out) completed the formalities for England who avenged their group-stage defeat by Australia at a venue where they had won 10 previous matches across all formats.
Roy, leading England's chase of Australia's 223, was batting on 85 when he attempted to pull Pat Cummins' short delivery and missed by a fair margin, as replays later confirmed.
As it became clearer that England were strolling, the party moved through the gears.
The opener launched Nathan Lyon's first ball back down the ground for his first six of the innings before slapping the spinner through backward point for another boundary, showcasing the full range of shots in his arsenal.
Roy smashed his fourth consecutive fifty in the tournament, clobbering Smith for three sixes in a row.
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Did his job. That first ball four settled the nerves and when Roy started driving Starc as well I knew the game was over.
Now comes the chance to be the first England team to win the World Cup and as the chants of "Cricket's coming home" rang out, there was little doubt the public believe Morgan's team can deliver. Morgan flat-batted a four to seal victory.
England's bowler Chris Woakes, left, celebrates with teammate England's Jos Buttler after dismissing Australia's batsman Mitchell Starc for 29 runs. The stump mics even caught a furious Roy yelling "that's f***ing embarrassing".
The former captain posted his highest score of the tournament with 85, but only a gutsy Alex Carey (46) provided any real support in a 103-run fourth-wicket stand.
Although Smith had looked nervy at the starts of his innings, making just seven off his first 34 balls, the No.3 brought up a 72-ball fifty - met by more boos than cheers from the partisan crowd.
Woakes won the man-of-the-match award at Edgbaston after taking 3-20 in a lethal eight-over spell that included the key wicket of opener David Warner.
England seamer Chris Woakes, who took 3/20 from eight immaculate overs, added: "I'm pretty speechless".