Joe Biden told "all people of the United Kingdom, our hearts go out to you", as he recalled fond memories with the Queen ahead of her funeral.
He told the late monarch's subjects they were fortunate to have had her for 70 years and her death "leaves a giant hole".
The US President was at Lancaster House to sign the book of condolence when he made the touching tribute in front of cameras.
He said: "We've had the opportunity to meet with an awful lot of consequential people, I can say that the ones who stand out in your mind are those whose relationship and interaction with you are consistent with their reputation.
"When the Queen had us to the castle for tea and we had crumpets, she kept offering me more, I kept eating everything she put in front of me.
"She was the same in person as her image - decent, honourable and all about service.
"My hearts go out to the Royal Family, to King Charles and all the family, it’s a loss that leaves a giant hole and sometimes you think you’ll never overcome it, but as I’ve told the King, she’s going to be with him every step of the way, every minute, every moment and that’s a reassuring notion.
"So to all the people of England, to all the people of the United Kingdom, our hearts go out to you and you were fortunate to have had her for 70 years, we all were, the world’s better for her."
Joe Biden and his wife Jill Biden paying their respects at the Queen's lying in state in Westminster Hall
Before heading to Lancaster House, Biden and First Lady Jill Biden paid their respects at the Queen's lying in state at Westminster Hall.
The couple - who touched down at Stansted Airport on Saturday evening - were spotted on the balcony of the hall on Sunday afternoon.
The US President has flown to the UK to attend the Queen's funeral, which takes place on Monday.
Barack Obama's message
Former US President Barack Obama praised the Queen's "very human quality of kindness and consideration" in a video message released to mark her funeral.
In the video, President Obama said that the first time he met the Queen, she reminded him of his own Grandmother.
The Queen was "very gracious," he said, adding that she had a "wry sense of humour" and was also "no nonsense."
"She could not have been more kind of thoughtful to me and Michelle," he said. "Shortly thereafter me and Michelle and Malia and Sasha, my two daughters, had occasion to go back to England."
"Buckingham Palace reached out and Her Majesty had invited Michelle and the two girls to tea."
"She had then offered the two girls to drive in her golden carriage around the grounds of Buckingham Palace."
"It was the kind of generosity and consideration that left a mark on my daughter's lives."
Obama, the first African-American President in US history, was in office between 2008 and 2016.
He met the Queen several times on visits to the UK, including at a private lunch with her and Prince Phillip at Windsor Castle in 2016.