It is the country’s first major trophy since the men’s team won the World Cup in 1966.
Ella Toone gave England the lead in the 62nd minute with a superb lob after being sent one-on-one with the German goalkeeper.
Image: England celebrate their tournament victory
The Lionesses couldn’t hold on as Germany’s Lina Magull scored a strike in the 79th minute.
But England prevailed in extra time as Chloe Kelly headed home from close range after Germany failed to clear a corner.
Speaking briefly to the BBC, Kelly said “it’s amazing” before running off to sing Sweet Caroline with her bandmates.
Returning briefly to the microphone, he added: “This is what dreams are made of. Wow, this is incredible.”
Image: Ella Toone scores England’s first goal
Captain Leah Williamson said: “We’ve been talking, talking, talking and we’ve finally got it done.”
Ella Toone said it was the ‘best day’ of her life and it ‘doesn’t seem real’.
Jill Scott, 35, who was brought on late in the second half, said the younger players “played with freedom” and the win was “absolutely fantastic”.
Men’s team captain Harry Kane tweeted: “Absolutely unreal scenes at Wembley!! Huge congratulations to the amazing lionesses!!”
Image: Captain Leah Williamson receives the trophy
Prime Minister Boris Johnson said: “Football has come home! A stunning victory by the lionesses. Football grounds across the country will be filled like never before with girls and women inspired by your triumph.”
In central London, huge celebrations took place in Trafalgar Square. Horns were honked and shouts of “he’s coming home” were heard.
It is the second consecutive title for coach Sarina Wiegman, who led the Dutch to victory in the competition in 2017.
Explaining the team’s success, he said they had “agreed on a few things about behavior and they weren’t just words, we lived them.”
He added: “The game was so tight, there was a bit of a battle in there but who cares, we won 2-1.
“We are European champions.”
Image: There was a huge turnout at Wembley
Former England international Gary Neville tweeted that Lyon’s win was a “seismic moment for sport in this country”.
Jamie Carragher said “they are all role models for future generations”.
The number of fans at Wembley to see the victory was 87,192 – a UEFA Euro tournament record.
Germany suffered a major blow before kick-off when their captain and striker Alexandra Popp was injured in the warm-up and forced to withdraw.
