Koci Selamaj, 36, from Eastbourne, East Sussex, pleaded guilty to murder at an Old Bailey hearing on Friday. The 28-year-old was found dead in Cator Park in Kidbrooke, south-east London, on September 18.
Selamaj drove to London from the south coast to carry out a pre-meditated attack on a woman with “extreme violence”.
The garage worker lurked around the park before targeting Ms Nessa as she passed through on her way to meet a friend on September 17 last year.
CCTV footage captured the moment Selamaj overwhelmed the 28-year-old by repeatedly striking her with a 2ft long weapon before carrying her away unconscious.
It is alleged that he then strangled her in undergrowth in what was suspected to be a sexually-motivated attack.
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.
Selamaj, an Albanian national, was arrested in Eastbourne and charged over her death on September 26.
At a previous hearing, Alison Morgan QC said: “The prosecution allege this was a premeditated and predatory attack on a stranger.”
Ms Morgan said the attack was carried out with “extreme violence”
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“In fact it was a weapon which appeared to break up during the course of the many strikes on the deceased.
“The CCTV footage shows the defendant then carrying the deceased, who appeared to be unconscious by that point, up a bank and effectively out of sight.”
Selamaj’s actions afterwards were out of camera shot, but Ms Nessa was not seen alive again.
Earlier this year, a lawyer for the Selamaj confirmed that he accepted being the person caught on CCTV and that he had hit Ms Nessa a number of times.
The murder of Ms Nessa heightened concern for the safety of women and girls in the capital following the stranger murders of Sarah Everard, and sisters Bibaa Henry and Nicole Smallman.
Previously, Ms Nessa’s family have said: “No family should ever have to go through this. We need our leaders to step up, and we need our communities to step up.
“We need our country to step up and stand with us and say no more violence against women.
“We also hope that everyone remembers Sabina as the joyful, happy, dedicated person that loved teaching and contributing to the community that she loved dearly.”