Underdogs Denmark took the lead through a Nadia Nadim penalty after just five minutes of the final, but the Dutch struck back quickly, Miedema slamming home Shanice van de Sanden's superb squared pass.
Lieke Martens then put the home side in front by curling in a bouncing shot, but Pernille Harder equalised before the break, cutting in from the right and rifling the ball home with her left foot.
The Dutch would not be denied however, and Sherida Spitse scored a free kick early in the second half before Miedema put the result beyond doubt with a brilliant run and finish in the 89th minute.
The Danes stunned the world of women's football when they ended Germany's 22-year reign as European champions, coming from a goal down to win 2-1 in the quarter-final to crush German hopes of a seventh successive title.
Spurred on by that victory, they beat Austria on penalties to reach the final where they showed the hosts no respect in the opening exchanges, and when Sanne Troelsgaard was brought down in the box, Denmark's Afghan-born striker Nadim confidently smashed the ball into the top corner.
It was the first time the Dutch had trailed in the tournament, but the setback was temporary.
Speedy winger Van de Sanden has tormented every opponent and her blistering run and pass set up Miedema for a simple finish in the 10th minute that brought the hosts back into the game.
In Martens, the Dutch have a superbly skilful two-footed player who curled the ball home to settle their nerves.
Hardly mentioned as contenders in the run-up to Euro 2017, the Dutch quickly showed themselves to be the strongest, fittest and most skilful team and, spurred on by raucous home crowds, have won every game.
Harder's equaliser was well-deserved, but Denmark ran out of steam and could not cope with the home side's seemingly limitless pace and power as they notched two second-half goals to secure the trophy.
The sight of the victorious players dancing on the pitch after the final whistle of a memorable final added a new celebratory chapter to this football-loving country.
The challenge now is to build a Dutch dynasty in the years to come.
(Reporting by Philip O'Connor, editing by Neil Robinson)
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