Koci Selamaj, 36, allegedly travelled to London from his home in Eastbourne.
A garage worker accused of murdering primary school teacher Sabina Nessa is expected to enter his plea later.
It is claimed he struck 28-year-old Ms Nessa as she walked through Cator Park in Kidbrooke, south-east, London, on her way to meet a friend on September 17.
The body of Ms Nessa, who taught a year one class at Rushey Green Primary School in Catford, was found nearly 24 hours later covered with grass near a community centre in the park.
It is believed that Ms Nessa’s attacker was a complete stranger to her.
Selamaj, from Eastbourne, East Sussex, was arrested in the seaside town and charged with her murder.
On Thursday, Selamaj, an Albanian national, will appear at the Old Bailey for a plea and directions hearing.
The defendant, who is in custody, will appear before senior judge, Mr Justice Wall.