The photographer, who was appointed a CBE by the Queen for services to art in 2001, was recommended to the palace by Downing St as part of its campaign to promote Britain worldwide.
Sajid Javid, the Culture Secretary, praised the portrait as helping to "showcase everything that is great about the UK to an international audience".
It is the first portrait of the Queen, who attended Easter Sunday service at Windsor, by Bailey. It follows a series of paintings and photographs by respected and diverse artists. Recent years have seen her sit for a starkly contemplative portrait by Chris Levine, with her eyes closed and crown on head, and a dramatic formal photograph by Annie Leibovitz in Buckingham Palace.
In 2002, she was photographed by the fashion photographer Rankin, who captured her in bright pink lipstick smiling in front of a Union flag to commemorate the Golden Jubilee, and described her as "funny and jokey".
Bailey's chosen photograph will now be used to promote the Government's GREAT campaign. He has previously praised the benefits of quick, natural photoshoots that capture personalities. Last year, he attributed his success to building a relationship with models, saying: "You just have to fall in love with people so they're the centre of your universe for that two or three hours you're with them."
His most recent exhibition, Bailey's Stardust at the National Portrait Gallery, saw him socialise with the Duchess of Cambridge as she attended a gala event as patron.
His career has seen him photograph some of the most famous faces in the world, including Diana, Princess of Wales, the Beatles, Sir Mick Jagger, Kate Moss, Jean Shrimpton, Terence Stamp, Sir Michael Caine and Johnny Depp.
The Queen has every reason to smile in her portrait as she begins her 89th year. The past year has seen her become a great-grandmother again, with the birth of Prince George to the Duke and Duchess of Cambridge and Mia to Zara Phillips and her husband, Mike Tindall.
The royal family have enjoyed unprecedented levels of support in Britain, and the Duke and Duchess of Cambridge's tour Downunder has been hugely popular. Prince Harry has carved out a role with military charities, the Duke of Edinburgh appears to have battled back from ill-health and the 60th anniversary of the Queen's coronation was marked by widespread celebration.