A crowd of 28,624 were in attendance as Wiegman's team delivered on the night, having gone out at the last-four stage in the last three major tournaments.
Following a shaky start for the Lionesses in which Sweden's Stina Blackstenius hit the bar, Beth Mead, already leading the race for the Golden Boot, put Sarina Wiegman's side ahead with a 34th-minute strike that took her to six goals for the tournament.
Lauren Hemp's cross ran right through to Lucy Bronze on the right side of the area, who passed it first time to Mead.
The Arsenal played had her back to goal but turned and fired past goalkeeper Hedvig Lindahl to give England the lead.
England went into the half-time break with a 1-0 advantage, although there had been danger signs for Wiegman's side throughout the opening period.
England doubled their lead early in the second half when Bronze headed home from a Mead corner.
There was a VAR check for offside, but replays showed Hemp was onside as the ball passed her on its way into the net.
England made it 3-0 with a stunning Alessia Russo backheel through the legs of the Sweden goalkeeper.
Russo had been brought on for Ellen White in the second half and had already set up Hemp, whose shot glanced over off the bar.
And in the 68th minute she struck, first having an effort well saved by Lindahl but then getting to the rebound and, with her back to goal, innovatively back-heeled the ball home.
Fran Kirby added a fourth, aided by a mistake from Sweden goalkeeper Lindahl.
Kirby tried her luck with a long-distance effort and the goalkeeper was unable to gather despite getting both hands to the ball, which trickled into the net.
England can now look forward to a showdown on Sunday with either Germany or France at a sold-out Wembley, where victory will secure them the first major trophy in their history.
It will be a third appearance in the competition's final after the runners-up finishes of 13 years ago - when they suffered a 6-2 loss to Germany - and at the inaugural Euros in 1984, which saw them beaten on penalties by Sweden.
Triumphing on Sunday would also mean back-to-back Euros successes for boss Wiegman, who, after overseeing her native Netherlands winning the 2017 edition on home soil and then reaching the 2019 Word Cup final, has had an England tenure that remains unbeaten after 19 matches, with 17 wins, 104 goals scored and only four conceded.
The sense the team are on the brink of something special was certainly tangible among England fans in the 28,624 crowd at the stadium, with chants of "football's coming home" reverberating around the ground at various points.