The 28-year-old criminology PhD student was picked up from the Monroe County jail around 6am ET on Wednesday morning, beginning his transfer into Idaho custody, according to NewsNation journalist Brian Entin.
It is not clear how he is being transported or when he will arrive.
On Tuesday afternoon, Mr Kohberger waived his extradition rights, paving the way for him to be transported from Pennsylvania to Idaho to face four charges of first-degree murder and one count of burglary.
The 28-year-old was shackled and handcuffed as he appeared for his extradition hearing at the Monroe County Courthouse in Pennsylvania.
He mouthed “I love you” to his tearful family members who were in court to support him before he signed documents agreeing to the extradition request.
The judge ordered him to be returned to Idaho within the next 10 days, giving authorities up until Friday 13 January – the two-month anniversary of the murders – to return him to the state.
Pennsylvania officials refused to divulge details about the transfer in a press conference on Tuesday saying that it was down to Moscow Police to arrange but that they hoped it would be “as soon as possible”.
Moscow Police vowed to keep the details of the move under wraps – including the timeline and the method of transportation – due to security concerns surrounding the high-profile prisoner.