They've said obtaining the endorsements came at great risk to all involved.
The journey to New York went via Geneva in late August when a British team swam with a symbolic version of the petition across the lake to the UN's Geneva office.
The 72 kilometre swim drew attention to the petition and to the hurdles ahead in getting it to the UN General Assembly.
The exiled West Papuan independence leader Benny Wenda has said he'll present the document to the Secretary General and the C24, the special committee on decolonisation.
He said there was a rigorous process underway to verify the thousands of signatures received so far from within Indonesia's Papua region.
"Indonesia's always saying it's just a handful of people that are talking about independence, it's just a dream and fantasy, but now we show that all the minorities are wanting independence," Wenda said.
"That means Indonesia's presence in West Papua is illegal."
Swimming across Lake Geneva has not been the only obstacle in getting the petition to New York.
Free West Papua campaigners have drawn attention to the 42 people they've said have been tortured and the two people who had been arrested in the Indonesian province as a direct consequence of the petition.
Campaigners said one of them was a member of the pro-independence National Committee for West Papua, the KNPB.
Yanto Awerkion was arrested on 23 June, according to Free West Papua campaigners, at a rally which promoted the petition.
They said he was still in custody after being charged with treason, a crime which can carry a life sentence in Indonesia.
The harsh treatment has driven many West Papuans into exile.
A representative from the Free West Papua Campaign in the Netherlands, Oridek Ap, said he fled the Indonesian occupied territory 34 years ago.
"I've never been back to Papua since Indonesia killed my father in 1984," said Ap.
"His death is my motivation to stand up for my people."
His father, the musician and anthropologist Arnold Ap, died in prison where he was being held without charges.
He was killed by a gunshot to the back.
Human rights groups and academics have estimated that more than 150,000 Papuans have died since the Indonesian occupation began in the 1960s.
Oridek Ap was among a group of exiled West Papuans in Geneva for the swim across the lake.
"We want to represent our people, the West Papuan people by singing and dancing to welcome the swimmers. That's why we're here, to support them."
Ap said his support represented those at home in West Papua and the 1500 living in exile in the Netherlands.
Another supporter was 21-year-old Harry Jenkinson from the UK.
The veteran campaigner had been involved since he was 14 and was in Geneva to organise the itinerary around the petition's swim team.
Jenkinson said it was a very emotional experience.
"The people of West Papua have been totally inspired by the swim, and last night we got information in photos that people were watching us on big screens in West Papua, live."
The spokesperson for the United Liberation Movement for West Papua, Benny Wenda, said he was confident the petition would open the eyes of the world to the need for an internationally supervised vote on independence for West Papua.
"Our voice has been hidden under the carpet nearly 50 years so this is an historical moment and we need to make sure that the petition will be handed over right."
The plebiscite by which Papua was incorporated into Indonesia in 1969 was sanctioned by the UN.
But, with just 1025 people, around 0.2 percent of the population at the time, participating under duress, the so-called Act of Free Choice was regarded by Papuans as illegitimate.
According to Wenda, there is an onus on the UN to correct this historical injustice and facilitate a legitimate self-determination process.
– Source: PACNEWS