And the former England star said he gets "goosebumps" every time he drove through the gates of her London residence.
Beckham was among star guests at a special ceremony to present medals to the 60 winners of The Queen 's Young Leaders Awards for 2016.
The project recognises and celebrates exceptional young people from across the Commonwealth who are taking the lead in their communities and using their skills to transform lives.
The Queen was joined at the event in the palace Ballroom by her grandchildren Prince Harry, Princess Beatrice and Princess Eugenie.
"I've been here a couple of times now and every time it is very special.
"After the school pick up today I was talking to Harper and I was like 'I'm going to see the Queen. '
"She was like, 'okay but do you think she will be drinking tea.' So she was very inquisitive. I am so proud to be here."
He added of the Euros: "All of us, minus Victoria, have been watching it. She doesn't watch too much of it.
"Harper just pops in and out. But me and the boys have been watching it a lot."
Also there was Chairman of The Queen Elizabeth Diamond Jubilee Trust, Sir John Major, shoe designer Jimmy Choo and Sir Lenny Henry.
Beckham added of the Young Leaders: "I want my children to be inspired by these guys.
"It's so nice to see these young men and women come here that are so passionate about what they want to do in life, their dreams, it's just something that's so special to them.
"The excitement in the palace was really incredible and it's amazing they get to meet Her Majesty and the chance to experience something like this."
This year's winners, aged between 18 and 29, are working on a range of issues including education, climate change, gender equality, mental health and improving the lives of people with disabilities.
In a speech, Harry praised his 90-year-old grandmother for the example she has set since she became monarch at such a young age, 63 years ago.
"As the head of the Commonwealth, the Nation, the Armed Forces and our Family, I - like millions of others across the world - have been able to look to her for inspiration and guidance.
"The Queen, who assumed the challenge of leadership at such a young age, has shown us all the importance of selfless commitment and service.
"She is the example I aspire to and the standard by which I will judge my contribution."
