Obama and Michelle will attend a private lunch hosted by Queen Elizabeth II at Windsor Castle on Friday, a day after her 90th birthday on April 21, before joining William and Kate for an informal dinner at their home in London the same day.
"Their Royal Highnesses are very much looking forward to welcoming President and Mrs Obama to Kensington Palace," a Kensington Palace spokesperson said.
Michelle is believed to have struck a close association with the British monarch since she ignored protocol to put her arm around the Queen during an official visit in 2009.
Obama will arrive in London on the evening of the Queen's birthday on Thursday and leave on Sunday.
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The US President will be in the UK as part of a tour of Saudi Arabia and Germany.
The referendum is to decide on Britain's possible exit from the European Union, dubbed 'Brexit.'
In Washington, White House Press Secretary Josh Earnest said the visit will allow President Obama to coordinate on today's most pressing international challenges with "one of our closest allies.