Police Chief Keith McCaskill called the search a "mammoth" task, as it will involve moving thousands of cubic metres of garbage, but he said Nepinak's family deserves closure.
"I know it's really difficult for the family," McCaskill told reporters on Wednesday.
"Can you imagine having your own loved one possibly being in the Brady Road landfill site? That's a horrendous thing for any family to go through."
Police believe Nepinak, 31, was slain by Shawn Lamb, who is also accused of killing two other aboriginal women within the past year.
Lamb, 52, was charged in June with three counts of second-degree murder in the deaths of Nepinak, Carolyn Sinclair, 25, and Lorna Blacksmith, 18.
Police have recovered the bodies of Sinclair and Blacksmith, but the body of Nepinak has yet to be located, despite numerous searches.
Investigators recently met with members of Nepinak's family and advised them that the investigation has led them to believe her remains were dumped in a garbage bin eight months ago in the city's West End area after her death.
The bin was then emptied at the landfill site. A portion of the landfill has been secured by police and is being prepared for the search.
'We believe she is there'
"We believe she is there, and we have strong belief in that," McCaskill said.
"It's one of those things that it's not an exact science here, but the best information we possibly have is that's where the body potentially is."
McCaskill said it will take at least a month, and possibly cost upwards of $500,000, just to remove enough garbage to access the search site.
He estimated the chances of finding Nepinak's remains — such as pieces of bone — are at less than five per cent.
"There is a mammoth amount of fill and garbage and things that have been put into that site … on a daily basis," he said.
McCaskill added that it will be a potentially dangerous task as searchers may come into contact with "everything from sharp needles to … animal parts to gases."
He noted that the landfill search will be different from the search through the Port Coquitlam, B.C., pig farm of Robert Pickton, who was convicted of killing six women.
"You can't use sifters, for instance, which they did at the Pickton farm; you can't do that," he said.
"It's got to be by hand and searching visibly on exactly what you're seeing there."
Provincial and municipal governments have promised they will help the police service cover the costs related to the search.
Nepinak's sister, Gail Nepinak, said police have known for weeks that remains may be at the landfill, but officers should have told the family earlier so that they would not have wasted time searching elsewhere.
Still, she said knowing the landfill search is going to happen is a tremendous relief.
"This is our only one chance to make sure that she [is] found and that she does come back and, you know, she's laid to rest the right way," she told reporters.
"If I have a chance to go there every day to search with them, I'd go with them, just to help them and make sure that they're doing a right job," she added.
The Assembly of Manitoba Chiefs said it applauds the Winnipeg Police Service's decision to search for Nepinak's body.
Officials said police have asked the assembly for volunteers to help with the search.
"We as a community have an opportunity to help find Tanya and bring her home," Grand Chief Derek Nepinak said in a release.
"She does not belong where she is. She needs to be found and given a proper burial with the honour and love she deserves."