The Queen was honoured with a 21-gun salute as she met President George W Bush in Washington DC on the final leg of her US visit.
President Bush joked with the Queen during her visit
Standing outside the White House, the Queen said Britain and America had a "close and enduring" friendship.
The president said the Queen was "a good person, a strong leader and a great ally".
Later the Queen will be guest of honour at a state banquet and will visit the Children's National Medical Centre.
The state visit has included trips to the site of the first permanent English settlement in the US and the famous Kentucky Derby horse race.
On her fifth visit to America, the Queen reflected on how "the stories of our two countries have been inextricably woven together".
She called the US a "great nation" and said it was time to "take stock of our present friendship".
"It is the time to look forward, jointly renewing our commitment to a more prosperous, safer and freer world," she added.
Mr Bush, meanwhile, joked with the Queen after making a mistake in his speech.
He said: "You helped our nation celebrate its bicentennial in 17... 1976" , and then joked the Queen had given him "a look that only a mother could give a child".
The president said the UK had "written many of the greatest chapters in the history of human freedom".
He said its relationship with the US was built "on the surest foundations - our deep and abiding love of liberty".
This was the Queen's fifth visit to the United States
The Queen was last in Washington in 1991 when George Bush Snr was the American president.
The White House said 7,000 guests were invited to the arrival ceremony for the Queen.
Film star Mickey Rooney, 86, greeted the Queen with a kiss on the hand and said afterwards he enjoyed meeting the monarch.
"It was a great thrill. She said she was happy to be here," he said.
Earlier in the trip, the Queen, accompanied by the Duke of Edinburgh, fulfilled a long-held ambition to watch the Kentucky Derby at Churchill Downs, Louisville.
Her visit to the first permanent English settlement in the US, in Jamestown, Virginia, marked its 400th anniversary.
In Virginia, the Queen extended her sympathies to those affected by the shootings at Virginia Tech last month.
The tour is the Queen's first carbon-offset state visit, where a donation is made to an environmental charity to offset the plane journeys made by the royal party.
On Monday night, 134 guests will return for a state dinner - the first in George W Bush's presidency to demand a white tie dress code.
The BBC's Washington correspondent Adam Brookes said it would be a "sparkling" affair.
THE QUEEN'S FIRST CARBON-OFFSET STATE VISIT
Total air miles
- 13,317 km or 8,275 milesAmount of CO2 emitted based on scheduled flights
- 1. 5 tonnesEstimated offset cost per person
- £13.20 to £14.18 ($26.22-$28.17) depending on type of offset package
Source: The Carbon Neutral Company carbon calculator