Raducanu beat fellow teenager Leylah Fernandez 6-4 6-3 to end Britain’s 44-year wait for a women’s Grand Slam singles champion.
“I send my congratulations to you on your success,” the Queen said.
“It is a remarkable achievement at such a young age, and is testament to your hard work and dedication.”
In a statement, the monarch added: “I have no doubt your outstanding performance, and that of your opponent Leylah Fernandez, will inspire the next generation of tennis players.”
UK Prime Minister Boris Johnson tweeted: “What a sensational match! Huge congratulations to Emma Raducanu.
“You showed extraordinary skill, poise and guts and we are all hugely proud of you.”
It was a historic night for British sport’s newest star which led pundits to predict big things and seemingly brought the UK to a standstill…
Virginia Wade, who was present at Arthur Ashe Stadium to witness Raducanu’s win, was the last British woman to win a Grand Slam singles title – at Wimbledon in 1977.
In an unprecedented run Raducanu became the first qualifier to win a major and has done so without dropping a set.
“A star is born,” tennis legend Martina Navratilova said. “Emma Raducanu makes history and she is just getting started.”
Former British number one Greg Rusedski, speaking to Amazon Prime, added: “She is going to be a multi-Grand Slam winner, a world number one.
“She is the real deal and it is a breath of fresh air having an 18-year-old win the event.”
Raducanu, whose run to the fourth round at Wimbledon earlier this summer is her only other Grand Slam appearance, will take home £1.8m in prize money and rise from 150th to 23rd in the world rankings.
Former Wimbledon champion Pat Cash described her success as “mindboggling”.
“This [a qualifier winning a Grand Slam] is something I never could have believed would happen,” the Australian said on BBC Radio 5 Live.
“I think I am going to wake up. It is so unbelievable. It is flabbergasting to see this performance.”
Tim Henman, another ex-British number one who was courtside in his role working for Amazon, said: “She will win more of these [Grand Slams], she is that good.
“This is not some flash in the pan or fairytale. She is playing ‘top-five tennis’.
“Her world will be turned upside down but she has good people around her and it will be a hell of a ride if she can stay injury free.”
Raducanu won the title with a classy performance in a high-calibre match against Canada’s Fernandez that lasted almost two hours.