According to the White House, Obama gave the queen a collection of rare memorabilia and photographs in a handmade leather-bound album that chronologically highlights her parents' visit to the United States in 1939.
That visit by King George VI and Queen Elizabeth was the first such trip to the U.S. by a reigning British monarch, and Obama's gift has both "historic and personal value," the White House said.
Obama's 2009 gift, an iPod loaded with photographs of the queen's 2007 visit to the United States, was panned by critics, as was a gift of DVDs he had given then-Prime Minister Gordon Brown.
On this more formal state visit, Obama also gave Prince Philip a custom-made set of Fell Pony bits and shanks, as well as original horseshoes worn by recently retired champion carriage horse Jamaica.
For Prince Charles, the president offered a special selection of plants, seedlings and seeds from the gardens of Mount Vernon, home of George Washington; Monticello, the home of Thomas Jefferson; and the South Lawn of the White House, as well as jars of honey from the White House beehive.
The queen gave the Obamas a collection of correspondence between various presidents and Queen Victoria, including one in response to the death of Abraham Lincoln. The first lady was also given an antique broach.
A spokesman for the queen said she has been intimately involved in planning the details of the state visit, and spoke of a sincere fondness between the two heads of state.
"Very warm words have been spoken between the royal family and the Obamas," the spokesman said. "There is a genuine, genuine -- and I really mean this -- a genuine warmth between the two families."