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Many on social media have said there were more than 40,000 people in the tickets queue.
The former US First Lady is appearing at the 2,900-seat venue on 3 December.
Tickets are appearing on Viagogo for thousands of pounds, but the venue said it has asked for them to be removed.
Any tickets bought from unauthorised third parties will not be admissable, the venue said.Obama will be discussing her memoir, Becoming, with award-winning novelist Chimamanda Ngozi Adichie.They will talk about her experiences from childhood, her work, motherhood and "her time spent at the world's most famous address".
She will also share "life lessons learned" while hoping to "inspire people to become the very best version of themselves".
People tweeted that they had been queuing since 4am at the venue.
The South Bank Centre, which is a multi-arts venue next to the River Thames, tweeted at 10:30GMT to say they had sold out.
The London date is in the middle of a 13 night tour starting on 13 November in the Obama's hometown of Chicago, where she will be in conversation with Oprah Winfrey.Tickets sold fast in the US and Obama tweeted she was "truly humbled by the response to my upcoming book tour".
The South Bank Centre said they are also in the process of identifying touted tickets.
They told the BBC that due to "extreme demand for this event, unfortunately there will be people who are disappointed".
But they added they had "worked hard to ensure that tickets are available to as wide an audience as possible, by limiting tickets to two per booker and ensuring there is a lower price point of £30."
Three hundred tickets have been held back to be given free to secondary school pupils in London and the UK, as well as local charities.
The South Bank Centre said they do not have exact figures for how many tried to get tickets.
A proportion of tickets went on sale yesterday for the venue's members, with the rest going on sale to the general public at 10am today.
