The inquiry, which could take two years to deliver its findings, is set to hear evidence of allegations that Zuma let ministries and government agencies be plundered for private gain in a scandal known as "state capture.”
Much of the probe is expected to focus on Zuma's relationship with the Guptas, a wealthy Indian family accused of wielding undue political influence.
An earlier report by a watchdog detailed allegations that Zuma ensured the Gupta family won preferential contracts with state companies, including huge mining deals, and were even able to choose cabinet ministers, Presstv reported.
Zuma himself appointed the inquiry in January on the orders of a high court, weeks before he was forced to resign from office as criticism grew from within the ruling ANC party.
Zuma's alleged involvement in multiple graft scandals damaged the party's image ahead of elections next year.
His successor President Cyril Ramaphosa has vowed to tackle corruption.
The inquiry will in part establish whether official appointments were "disclosed to the Gupta family or any other unauthorized person before such appointments were formally made," said inquiry head Raymond Zondo, the country's deputy chief justice.
Although the inquiry does not have powers to arrest or prosecute, it can refer matters for possible criminal investigation.
"At the heart of the investigation is whether outsiders influenced government or state-owned enterprises for selfish gain," said the commission's lead lawyer Paul Pretorius on the inquiry's opening day.
State funds looted
Pravin Gordhan, a former finance minister now responsible for state companies, has estimated that around 100 billion rand ($6.8 billion) of state funds may have been looted through corrupt awarding of government tenders.
Gordhan is among those expected to give evidence, along with his former deputy Mcebisi Jonas.
Jonas has alleged he was taken by Zuma to the Guptas' home in Johannesburg, where Ajay Gupta said he would be appointed finance minister.
When Jonas refused, Ajay allegedly offered him 600 million rand and asked if Jonas had a bag to take away 600,000 rand in cash immediately.
Pretorius said the commission would probe whether Zuma violated the constitution "by facilitating the unlawful awarding of tenders of state-owned enterprises."
Zondo vowed a thorough investigation and called for members of the public to submit their own evidence, but he expressed disappointment at the lack of cooperation from government officials.
The local Sunday Times said Zuma has been invited to appear, but the commission's spokesman declined to comment.
Zuma and the Guptas deny any wrongdoing.
"I hope that the inquiry gets to the bottom of how the South African state was captured in the way it was and what can be done to prevent this from happening again," David Lewis, executive director of South Africa's non-profit organization Corruption Watch, told AFP.
Zuma, 76, was forced to resign in February when ANC lawmakers turned against him.
The former president also has been charged with 16 counts of graft linked to an arms deal from before he became president.