The Pretoria High Court was due to decide whether he should be handed over to the International Criminal Court which charged him with the crimes.
Mr Bashir was in Johannesburg for an African Union (AU) summit.
A news conference will be held in Sudan’s capital upon his arrival.
On Sunday, a judge barred Mr Bashir from leaving until the arrest application had been considered.
Mr Bashir is accused of committing war crimes, crimes against humanity and genocide during the Darfur conflict.
The UN says that about 300,000 people in Sudan have died and more than two million have fled their homes since fighting began in 2003.
Government forces and allied Arab militias are accused of targeting black African civilians in the fight against the rebels.
At the hearing at the Pretoria High Court, the lawyer representing the South African government says Mr Bashir’s name was not on the list of passengers who took off earlier.
It is unlikely that South Africa will face sanctions for allowing Mr Bashir to leave the country even after a court order barred him from leaving the country, says the BBC’s Nomsa Maseko in Pretoria.
A number of African countries have in the past taken a decision not co-operate with the ICC as the court is seen to be racist and biased against African leaders.
So as things stand, Mr Bashir appears to have left South Africa with the blessing of the African Union, our correspondent says.
On Monday, UN Secretary-General Ban Ki-moon said the ICC’s warrant for the arrest of Mr Bashir must be implemented by countries who have signed up to the court’s statutes.
As a member of the ICC, South Africa is obliged to arrest anyone charged by the court.
Before the summit, the ICC issued a press statement urging the South African government “to spare no effort in ensuring the execution of the arrest warrant”.