The first couple will spend two nights at the palace after arriving in England late Monday night.
The queen and her husband Prince Philip greeted the Obamas at the majestic palace on a sunny, windy afternoon in London. Following a private tour, the two couples emerged on the ceremonial steps of the West Terrace for a 41-gun salute.
The president will meet with British officials during his two-day state visit.
The Obamas also already had a brief meeting with newlyweds, William and Katherine, the Duke and Duchess of Cambridge.
The queen hosted lunch for the Obamas at the palace, and the Obamas then laid a wreath at Westminster Abbey and heard the Choir of Westminster Abbey sing.
A palace official said the queen was closely involved and interested in the planning of this state visit, a grand display of royal pageantry that only happens about twice a year for a world leader of the queen's choosing.
Obama's visit is only the second official state visit by a U.S. president, according to Buckingham Palace.
As is customary, there was an exchange of gifts. The Obamas game the queen a collection of memorabilia and photographs from her parents' 1939 visit to the United States, while the queen gave the Obamas a selection of letters from the royal archives to and from past U.S. presidents and English monarchs. Mrs. Obama also received an antique brooch made of gold and red coral in the form of roses.
Obama was to meet briefly with British Prime Minister David Cameron on Tuesday, though their most substantial talks will come the following day, when Afghanistan, Libya and the global economy are all on the agenda.
After his two-day stop in Britain, Obama will head to France for a meeting of the Group of Eight industrialized nations and then to Poland, a schedule the White House says the president intends to keep despite the approaching ash cloud.
The Associated Press contributed to this story.