Adrian Ernest Bayley, 41, of Coburg, is contesting the one murder and three rape charges laid against him.
Jill Meagher disappeared from a busy Brunswick street after a night out with colleagues last September.
Her body was found in a shallow grave near Gisborne, north-west of the city.
Jill Meagher's husband Tom, her parents George and Edith McKeon and her brother Michael are in court for the committal hearing.
The court is full and security screens have been placed around the dock.
Last week Bayley's lawyers expressed concern about the "almost unprecedented" level of public interest in the case, referring to both the traditional and social media coverage expressing public anger over Ms Meagher's death.
Magistrate Felicity Broughton told the court she expects the hearing to be held in an "appropriate and dignified manner."
The court was told some material described as extremely distressing and sensitive may not be made public.
Prosecutor Gavin Silbert SC gave a brief opening in the case.
He told the court Ms Meagher was accosted by Bayley on Sydney Road in Brunswick, just eight minutes after she left a bar where she had been drinking with ABC colleagues.
The court heard at 1:38am he dragged her into a lane and raped and strangled her.
Mr Silbert told the court that Bayley left her body in the lane and returned home to get a shovel and his car.
He returned at 4:22am and it is alleged he drove to Gisborne and left Ms Meagher's body on the side of a dirt road.
The court heard during a 10-hour police interview Bayley admitted to raping and strangling Ms Meagher.
Ms Meagher's husband was not in court when Bayley arrived in the dock and was not in court as the details of what happened to his wife were read out.
Mr Silbert alleged Bayley killed Ms Meagher because she as the only witness to his crime.