Ms Kelty was 42 days into her trip when she went missing, and she had posted about passing boats full of men with arrows and rifles.
Ms Kelty, whose family are believed to live in Taunton, Somerset, had been attempting a 4,000-mile trip along the Amazon river from its source to the Atlantic Ocean and had been documenting her trip on Twitter.
According to the chief of the Amazonas state police, Ivo Martins, the murder had been committed with the intention of robbery, after the men reportedly attempted to sell their victim's GoPro, her tablet computer, and her two mobile phones.
Emma Kelty, a 41-year-old British primary school principal, was last heard from when she triggered a distress signal on September 13 in a notoriously unsafe stretch of the Amazon, The Guardian reports.
Three days before she disappeared, she posted: "So in or near Coari (100km away) I will have my boat stolen and I will be killed too".
Police said the canoeist came into difficulty last week when she activated an emergency locator device when she was between the towns of Codajas and Coari, 150 miles west of Manaus.
The navy also said her kayak and some personal belongings have been recovered.
According to local reports, the stretch of river she had been trying to travel on is a known route for bandits and drug traffickers.
A Foreign office spokesman said on Tuesday: "We are supporting the family of a British woman following her death in Brazil and are in contact with the Brazilian authorities".
Olie Hunter Smart, an explorer who completed a similar route in 2015 and helped Ms Kelty plan her journey, said Coari was known to be a unsafe area.
Mr Smart described her as an "incredibly fearless and courageous person". "Nice", Ms Kelty posted on September 10 as she entered a risky stretch of the river. In a blog written before she left, she said: "I have had folks, friends and strangers telling me not to do it, it's stupid, it's too unsafe. and I will die".
A year ago police chief Thiago Garcez, whose body has never been found, was said to have been murdered by drug-runners in the area where Ms Kelty disappeared.