In her speech, she spoke of the "new challenges" the US and the UK face in the 21st century, and stressed the bonds between the two countries.
"The anniversary of D-Day reminds us of all that our countries have achieved together," she said.
Watch The Queen and Donald Trump's speeches here:
The Queen continued: "Mr President, as we look to the future, I am confident that our common values and shared interests will continue to unite us.
"Tonight we celebrate an alliance that has helped to ensure the safety and prosperity of both our peoples for decades, and which I believe will endure for many years to come."
The Queen finished by inviting the room to raise a toast to the "continued friendship between our two nations, and to the health, prosperity and happiness of the people of the United States".
Mr Trump appeared to breach accepted royal protocol by touching the Queen on the back as she rose for his toast.
The US President paid tribute to the Queen as embodying "the spirit of dignity, duty, and patriotism that beats proudly in every British heart".
He said: "From the Second World War to today, Her Majesty has stood as a constant symbol of these priceless traditions."
He continued: "On behalf of all Americans, I offer a toast to the eternal friendship of our people, the vitality of our nations and to the long cherished and truly remarkable reign of Her Majesty, the Queen. Thank you."
Earlier Prince Charles and the Duchess of Cornwall welcomed Mr and Mrs Trump in the garden for tea at their official residence in the afternoon of the first day of the president's state visit.
The two couples posed for a picture in the morning room before moving to private quarters for tea.
At one point, the US President appeared to show where Charles should stand for the photographs - prompting Charles to look at little put out and Camilla to wink at members of the press.
The US President and Mrs Trump had earlier arrived by helicopter at Buckingham Palace and were greeted by Prince Charles and Camilla, as they stepped off Marine One.