Dewani, 34, denies ordering the killing of his 28-year-old Swedish bride Anni in Cape Town in November 2010, and has been fighting extradition from Britain ever since.
He claimed he had mental health problems, including depression and post-traumatic stress, and has been detained in hospital under mental health legislation.
But a British court ruled last month that after numerous legal challenges, he could be sent to South Africa.
Dewani flies out on Monday evening and will land in Cape Town on Tuesday morning, where he will be taken directly to the Western Cape High Court to be formally charged.
On the flight, he will be accompanied by a doctor, a nurse and police officers, the South African justice ministry said, given that he is “currently a patient and suspect who is in police custody and may need medical assistance en-route”.
Anish Hindocha, Anni’s brother, said the delay in extraditing Dewani had been “very frustrating” but expressed hope that he would finally see justice for his sister.
“It has been very difficult for my family,” Hindocha told ITV television, wearing a photograph of Anni Dewani pinned to his jacket with a pink ribbon around it.
“We are just focusing on this case at the moment and it is hard to even start to make the grieving process for Anni yet because there are so many questions we need answers to.
“It has been a nightmare. I can’t sleep at night, I can’t even work – the only focus I have is getting justice for her.
“We hope we get it and now today he is getting extradited and that is one step closer towards what we are seeking for her, that is justice for her.”
After the court hearing, scheduled for 11:30am (0930 GMT), Dewani is expected to be taken to the high security Valkenberg psychiatric hospital in Cape Town where he will stay until his fate is decided.
Members of Anni Dewani’s family are planning to attend the trial, and Hindocha said supporters had offered them free accommodation in South Africa.
“People are being very, very supportive,” he said.
Dewani claimed he and his bride were kidnapped at gunpoint as they drove through the Gugulethu township in a taxi.
A South African man, Xolile Mngeni, was jailed for life for the murder in December 2012. Two other men jailed over the killing allege that Dewani ordered the hit.