The agreement, signed at Number 10 Downing Street during a ceremony also attended by Britain's Olympics Minister Tessa Jowell, will allow organisers in Rio de Janeiro to learn from London's experience of hosting the 2012 Games, including on how to deliver a legacy that benefits the whole country.
A spokesman for Brown said: "As this is the first time a South American country will host the summer Olympics, this agreement will establish a structured cooperation programme which will allow the UK and Brazil to share knowledge and experience."
British firms will be hoping to successfully tender from some of the $50 billion (£30 billion) worth of infrastructure investment projects at stake in Brazil as it prepares to host the 2014 World Cup and 2016 Olympics.
Lula met business leaders in London to urge them to invest in Brazil, saying it was a country with "enormous challenges" but huge opportunity.
Brazil officially emerged from recession in the second quarter of this year - unlike Britain, where the downturn continues - and is expecting full-year GDP growth of between 0.1 and 1.0 per cent.
Lula also met Queen Elizabeth for talks at Buckingham Palace.
Before leaving London tonight, Lula also received an award at a gala dinner from the prestigious Chatham House think-tank for making "the most significant contribution to the improvement of international relations" over the past year.
During a trip to London in April for the G20 Summit Lula extended his stay in the capital so he could be given a tour of the Olympic Park.
April 2009: Brazilian President visits London's Olympic Park