Zuma resigned from the Cabinet on Thursday, after days of speculation over whether he would step down.
He will become acting president in place of President Jacob Zuma, a move that has prompted concerns from opposition parties and civil society groups that he may be using the Presidency as a political platform to pursue his agenda.
Zuma, who had been the Cabinet secretary for three months, resigned on Thursday after the Constitutional Court dismissed his nomination as acting President and dismissed his impeachment charges against him.
The court has previously said it will not be able to hear his impeachment proceedings because he was ineligible to be a President at the time of the alleged offences.
As of midnight on Thursday night, the Constitutional court said it would not be accepting Zuma’s impeachment charges and that Zuma should resign.
Zulu was sworn in as the new President on Sunday.
The Constitutional Court said Zuma could not be removed from office, but it said he should step down immediately as the country was in a state of emergency.
It said Zama should leave the Presidency and not use it as a platform to continue his political agenda.
Zuma has faced allegations of corruption in the run up to his inauguration in 2019, but his party denied he had any links to the alleged wrongdoing.
He was the first African leader to be impeached for the alleged crimes.
Zimbele, who served as president from 1996 until 2019, was widely seen as the favourite to succeed Zuma.
In an interview with the BBC, Zimbelem, who is also a former African Union (AU) commissioner, said Zimba was “the only African leader in the history of the African Union” who was “legally fit to be President”.
Zimba had said in December that he would not stand for the presidency and would stay in his role as the Cabinet Secretary.