Cameron's invitation to visit Britain and will spend a week there from June 18, officials accompanying Cameron at a summit of the Group of Eight leading economies in the United States told reporters.
Pro-democracy leader Aung San Suu Kyi walks to take an oath in the lower house parliament in Naypyitaw. Reuters/Soe Zeya Tun
Suu Kyi's party, the National League for Democracy, said last month she would visit Norway and Britain in June, but it was the first time the British government had confirmed the trip.
Suu Kyi will give a speech to both houses of parliament during her stay, a rare honour accorded in the past to figures such as former South African President Nelson Mandela and, last year, to U.S. President Barack Obama.
Her journey caps months of dramatic change in Myanmar, including a historic by-election on April 1 that won her a seat in a year-old parliament that replaced nearly five decades of oppressive military rule.
Her trip is expected to include a visit to the British city Oxford, where she attended university in the 1970s.
Suu Kyi, 66, was first detained in 1989, and spent 15 of the next 21 years in detention until her release from house arrest in November 2010. She refused to leave the country during the brief periods when she was not held by authorities, for fear of not being allowed to return.
Cameron invited Suu Kyi to visit Britain when he met her in Yangon in April. Her British husband, Michael Aris, died of cancer in 1999.
Britain is proposing the creation of an international commission to encourage "responsible" trade and investment in Myanmar, also known as Burma, now that sanctions on the country are being lifted, British officials said.
The plan is designed to help make sure trade benefits all Myanmar's people, rather than a "select few", a British official said.
The United States, the European Union, Japan, Canada and Australia have all moved in recent weeks to ease or suspend sanctions on Myanmar, as the once pariah nation embarks on democratic reforms and seeks engagement with the world.
British officials said Cameron would outline proposals at the G8 for a Commission for Responsible Investment in Burma that could bring together representatives from the World Bank and the Organisation for Economic Cooperation and Development, international companies and human rights campaigners.
The panel would establish principles that businesses would be encouraged to sign up to when trading with or investing in Myanmar, the officials said.