Ms Suu Kyi said it was particularly poignant for her to meet the party as it was a Labour prime minister - Clement Attlee - whom her father met in London in 1947 to seal an agreement for Burmese independence.
Ed Miliband hailed Aung San Suu Kyi as "the most famous opposition leader in the world" as the Burmese pro-democracy campaigner opened Labour's new London headquarters today.
She unveiled a plaque at the office building before joining the Shadow Cabinet for its weekly meeting.
Delivering a historic address to a joint session of both Houses of Parliament, Aung San Suu Kyi said she was seeking practical help to address the problems still besetting her country.
The Nobel peace laureate received a standing ovation from MPs and peers in a packed Westminster Hall, and said the key to reform was the establishment of a strong parliamentary institution.
Aung San Suu Kyi received a standing ovation as entered Westminster Hall which was packed with MPS, Lords and guests.
Labour MP Jonathan Reynolds has tweeted the following picture of the programme ahead of Aung San Suu Kyi addressing both houses of Parliament this afternoon:
Welcoming Aung San Suu Kyi to Downing Street, David Cameron has highlighted three ways that Britain will help Burma:
We will invest in strengthening Burma's emerging democracy.
We must address the ethnic conflicts. We're investing £3 million in immediate peace building work.
We must build an economic future for all of Burma's people.
David Cameron has welcomed Aung San Suu Kyi to Downing Street.
The Prime Minister said: "When we met in your house in Rangoon two months ago this visit to Britain was still a fragile hope."
Aung San Suu Kyi has planted a tree to commemorate her visit to Clarence House. The Burmese pro-democracy leader met Prince Charles and the Duchess of Cornwall during her historic return to the UK.
A wonderful visit to @clarencehouse by Aung San Suu Kyi who has planted a tree in the garden here today.