Mugabe, 91, who was accompanied by his wife Grace, has visited South Africa regularly in the past but his two-day stay will be his first official state visit in 21 years.
Zimbabwe's economy has been on a downturn for more than a decade due to low growth, low liquidity and high unemployment.
In March, the International Monetary Fund said that the country faced a "difficult" economic outlook with growth set to weaken again this year.
The Zimbabwean officials said it was in the interest of South Africa to help grow its neighbour's economy to stop the tide of economic refugees who have crossed the border seeking work.
Zimbabwe's economy entered a tailspin after the launch of controversial land reforms 14 years ago. By 2008, inflation had officially peaked at 231 million percent before the government stopped counting.
The South African government said President Jacob Zuma and Mugabe would hold talks today before a bilateral business forum scheduled for tomorrow.
"Due to its geographical proximity to South Africa, Zimbabwe's political and economic situation has a direct impact on South Africa."
Mugabe's wife Grace is seen as one possible successor to her husband, who came to power in 1980.
Former vice-president Joice Mujuru was long considered likely to take over, but she fell out with the veteran leader late last year and was sacked in December.
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