FIFA's executive committee chose South Africa, the slight favourites, on the first round of voting. The other candidates to host the 32-team finals were Morocco and Egypt.
Libya's bid was stood down by FIFA on Saturday because it did not meet the criteria and Tunisia pulled out on Friday after being refused the option of co-hosting the event with Libya.
The World Cup is the biggest sporting event outside the Summer Olympics and soccer the world's most popular sport.
Almost four years ago Germany controversially won the race to host the 2006 finals by a single vote after Oceania delegate Charles Dempsey defied orders to vote for South Africa.
FIFA president Sepp Blatter made it clear then that he wanted Africa to get the World Cup at the next opportunity as world soccer's governing body decided to rotate the finals around the continents.
South Africa hosted the 1995 Rugby World Cup and the 2003 Cricket World Cup successfully but the soccer World Cup, which began in 1930, has never been held on the continent.
Former president Nelson Mandela said last week that hosting the 2010 World Cup finals would be a perfect gift for the country as it celebrates 10 years of democracy.
He said it would add three billion rand (240 million pounds) to the economy and create more than 150,000 jobs in a country where unemployment is over 30
South Africa sent a high-profile mission to Switzerland, led by Mandela, President Thabo Mbeki and Nobel Peace prize winner Archbishop Desmond Tutu, and was the slight favourite.
HOPES BOOSTED
The country's hopes of success were boosted at the start of the month after FIFA inspectors rated its facilities as the best of five competing countries.
South Africa's bid was described as "excellent", while those of north African rivals Egypt and Morocco were "very good".
Morocco suffered a major blow by having questions raised about the country's lack of infrastructure.
Libya, whose hopes of co-hosting the finals with Tunisia had been repeatedly slapped down by Blatter, were taken out of the running by FIFA on Saturday before voting even began.
FIFA's technical evaluation report said Africa was prepared to host the finals but would need support in stadium plans, pitch quality, ticketing, budgeting and general planning.
The inspectors said South Africa had excellent overall infrastructure and a clear and stable bid project.
"Despite questions about security in the country, the legacy compared to the investment needed will be a great contribution to the country," the inspectors reported.
The World Cup finals, held in Asia for the first time when South Korea and Japan co-hosted the 2002 tournament, will be awarded to South America in 2014 with Brazil expected to land the finals when it celebrates its federation's centenary.