Selamaj ran up behind her and hit her over the head 34 times with a 2ft-long metal traffic triangle.
An “evil” sexual predator has been jailed for at least 36 years for the murder of primary school teacher Sabina Nessa.
The garage worker targeted 28-year-old Ms Nessa as she walked through Cator Park in Kidbrooke, south-east London, to meet a friend at 8.34pm.
CCTV footage captured the moment Selamaj ran up behind her and hit her over the head 34 times with a 2ft-long metal traffic triangle.
He carried her unconscious body up a grassy bank and out of view.
He then pulled up her clothes, removed her tights and underwear, and strangled her before covering her body in grass.
Ms Nessa, who taught a year one class at Rushey Green Primary School in Catford, was found nearly 24 hours later near a community centre in the park.
Days later, Selamaj, from Eastbourne, East Sussex, was arrested in the seaside town and pleaded guilty to murder in February.
On Friday, Selamaj refused to come to the Old Bailey and was jailed for life in his absence.
Mr Justice Sweeney set a minimum term of 36 years for the “savage” sexually motivated attack.
He said Ms Nessa was the “wholly blameless victim of an absolutely appalling murder which was entirely the fault of the defendant.”
Her death added to “the sense of insecurity” particularly felt by woman walking through the city at night.
“She had every right, as her family said, to be walking through the park all glammed up and out to enjoy herself after a long week at work.”
“The defendant robbed her and them of her life,” he said.
The judge noted the defendant’s guilty plea and lack of previous convictions.
But he added: “It is a striking feature of the defendant’s case that, clearly deliberately, it is not suggested by him that he had any remorse for what he did to Sabina Nessa.”
The judge said it was “cowardly” of the Albanian national to refuse to attend his sentencing but said he had no power to force him.
Ms Nessa’s sister, Jebina Yasmin Islam, described the murderer as “vile”.
She said: “The thought that he was waiting for some woman, to attack her and do what he wanted to do – I was just thinking what a horrible animal, (what a) vile animal he is.”
Following the sentencing, Metropolitan Police Detective Chief Inspector Neil John described Selamaj as an “evil coward”.
Commenting on the fact Selamaj had no previous convictions, he said: “It is highly unusual for someone to go from zero to a crime of this magnitude.
“We are pleased Selamaj will spend the majority of his life in prison.”
Addressing her absent killer on Thursday, Ms Nessa’s parents Abdur Rouf and Azibun Nessa said in a statement: “You had no right to take her away from us in such a cruel way.
“The moment the police officer came to our house and told us she was found dead our world shattered into pieces.
“How could you do such a thing to an innocent girl walking by, minding her own business.
“You are not a human being, you are an animal.”
Head teacher Lisa Williams described the “devastating” impact on Ms Nessa’s colleagues and students.
Earlier, prosecutor Alison Morgan QC said Selamaj had been violent towards his ex-partner in the past, including throttling her a number of times.
Three days before the attack on Ms Nessa, the defendant booked a room at the five-star Grand Hotel in Eastbourne, East Sussex, just five minutes from his home.
At about 2.20pm on September 17, hotel staff alerted police via 101 after Selamaj checked in to his £325-a-night room.
Police said they had been concerned about his demeanour and the fact he lived close by.
Selamaj went on to contact his former partner in a failed bid to persuade her to have sex with him.
She said in a statement that he appeared “very agitated” when they met in his car near the hotel.
The defendant then drove his Nissan Micra to Brighton and on to Kidbrooke in south London.
He used his bank card at Sainsbury’s to buy a rolling pin, chilli flakes and an energy drink.
He rejected the rolling pin as a weapon in favour of the traffic triangle, which he was to use to attack Ms Nessa.
He entered Cator Park shortly after 8pm and lay in wait for half-an-hour before Ms Nessa arrived en route to The Depot bar where she was due to meet a friend.
Ms Morgan said Ms Nessa had expressed concern about being in the park after dark but decided to use the cut through that night because she was running late.
In grainy footage played in court, Selamaj was seen running up behind Ms Nessa and launching a ferocious attack with the 2ft long traffic triangle.
As he carried her up a grassy hill, they went out of shot for 20 minutes.
Before leaving the park, he picked up pieces of the warning triangle and used wet wipes to clean a park bench near to where he launched his initial attack.
En route back to the south coast, Selamaj dumped the warning triangle in the River Teise in Tunbridge Wells, Kent.
Police said Selamaj appeared to be “calm and collected” on his arrest.
On being cautioned through a translator, Selamaj said: “What will happen if I open up now and say everything?”
In mitigation, Lewis Power QC had said Selamaj had provided no explanation for why he killed Ms Nessa, adding: “He simply accepts that he did it.”
Ms Nessa’s family hugged supporters as they left court.
Home Secretary Priti Patel said: “Sabina Nessa cruelly lost her life following the harrowing and callous actions of a man who is rightly now behind bars.
“Whilst I cannot possibly know how Sabina’s family and friends are feeling, I hope today’s sentence brings them a small comfort, knowing that this evil monster has faced justice.
“As Home Secretary, tackling violence against women and girls is central to my Beating Crime Plan and I am doing everything in my power to target perpetrators, protect the public and make our streets safer for everyone.”